mirror nuclei

We propose a high-statistics measurement of few body nuclear structure and short range correlations in quasi-elastic scattering at 6.6 GeV from 2 H, 3 He and 3 H targets in Hall B with the CLAS12 detector. We will measure absolute cross sections for (e, e p) and (e, e pN ) quasi-elastic reaction channels up to a missing momentum pmiss ≈ 1 GeV/c over a wide range of Q 2 and xB and construct the isoscalar sum of 3 H and 3 He. We will compare (e, e p) cross sections to nuclear theory predictions using a wide variety of techniques and N N interactions in order to constrain the N N interaction at short distances. We will measure (e, e pN ) quasi-elastic reaction cross sections and (e, e pN )/(e, e p) ratios to understand short range correlated (SRC) N N pairs in the simplest non-trivial system. 3 H and 3 He, being mirror nuclei, exploit the maximum available isospin asymmetry. They are light enough that their ground states are readily calculable, but they already exhibit complex nuclear behavior, including N N SRCs. We will also measure d(e, e p) in order to help theorists constrain non-quasielastic reaction mechanisms in order to better calculate reactions on A = 3 nuclei. Measuring all three few body nuclei together is critical, in order to understand and minimize different reaction effects, such as single charge exchange final state interactions, in order to test ground-state nuclear models. We will also measure the ratio of inclusive (e, e ) quasi-elastic cross sections (integrated over xB) from 3 He and 3 H in order to extract the neutron magnetic form factor G n M at small and moderate values of Q 2 . We will measure this at both 6.6 GeV and 2.2 GeV. Simulations and previous experience with CLAS12 show that we can obtain meaningful statistics with 55 days of beam time. We request 20 beam days each on 3 He and 3 H, and 10 beam days on 2 H at an incident beam energy of 6.6 GeV. We request an additional 5.5 days of beam time at 2.2 GeV to measure G n M at low Q 2 . Our proposed measurements will significantly constrain nuclear models for few body nuclear dynamics and short range structure. Also, we will measure the behavior of the neutron magnetic form factor at low to moderate Q 2 . This experiment will use the base equipment for CLAS12 and requires the construction of a new 3 H target. The JLab Target Group has a preliminary target design. The groups working on this experiment bring previous experience working with a 3 H target in Hall A.

We propose a high-statistics measurement of few body nuclear structure and short range correlations in quasi-elastic scattering at 6.6 GeV from 2 H, 3 He and 3 H targets in Hall B with the CLAS12 detector. We will measure absolute cross sections for (e, e p) and (e, e pN ) quasi-elastic reaction channels up to a missing momentum pmiss ≈ 1 GeV/c over a wide range of Q 2 and xB and construct the isoscalar sum of 3 H and 3 He. We will compare (e, e p) cross sections to nuclear theory predictions using a wide variety of techniques and N N interactions in order to constrain the N N interaction at short distances. We will measure (e, e pN ) quasi-elastic reaction cross sections and (e, e pN )/(e, e p) ratios to understand short range correlated (SRC) N N pairs in the simplest non-trivial system. 3 H and 3 He, being mirror nuclei, exploit the maximum available isospin asymmetry. They are light enough that their ground states are readily calculable, but they already exhibit complex nuclear behavior, including N N SRCs. We will also measure d(e, e p) in order to help theorists constrain non-quasielastic reaction mechanisms in order to better calculate reactions on A = 3 nuclei. Measuring all three few body nuclei together is critical, in order to understand and minimize different reaction effects, such as single charge exchange final state interactions, in order to test ground-state nuclear models. We will also measure the ratio of inclusive (e, e ) quasi-elastic cross sections (integrated over xB) from 3 He and 3 H in order to extract the neutron magnetic form factor G n M at small and moderate values of Q 2 . We will measure this at both 6.6 GeV and 2.2 GeV. Simulations and previous experience with CLAS12 show that we can obtain meaningful statistics with 55 days of beam time. We request 20 beam days each on 3 He and 3 H, and 10 beam days on 2 H at an incident beam energy of 6.6 GeV. We request an additional 5.5 days of beam time at 2.2 GeV to measure G n M at low Q 2 . Our proposed measurements will significantly constrain nuclear models for few body nuclear dynamics and short range structure. Also, we will measure the behavior of the neutron magnetic form factor at low to moderate Q 2 . This experiment will use the base equipment for CLAS12 and requires the construction of a new 3 H target. The JLab Target Group has a preliminary target design. The groups working on this experiment bring previous experience working with a 3 H target in Hall A.

The structure of 17 C is used to define a nuclear interaction that, when used in a multichannel algebraic scattering theory for the n+ 16 C system, gives a credible definition of the (compound) excitation spectra. When couplings to the low-lying collective excitations of the 16 C-core are taken into account, both sub-threshold and resonant states about the n+ 16 C threshold are found. Adding Coulomb potentials to that nuclear interaction, the method is used for the mirror system of p+ 16 Ne to specify the low-excitation spectrum of the particle unstable 17 Na. We compare the results with those of a microscopic cluster model. A spectrum of low excitation resonant states in 17 Na is found with some differences to that given by the microscopic-cluster model. The calculated resonance half-widths (for proton emission) range from ∼ 2 to ∼ 672 keV.

Charge radii of mirror nuclei are calculated by implementing pairing effects with the Hartree-Fock Bogoliubov approximation. Correlations between the difference of charge radii (∆R ch) and slope of nuclear symmetry energy (L) are examined for different mirror nuclei pairs of varying masses using 40 different Skyrme energy density functionals. ∆R ch − L correlations are found to be robust for the binding constraints imposed on density functionals. We observe that ∆R ch and L show better correlations in relatively heavier pairs than those obtained in the lighter pairs. Our calculations impose a constraint on the slope of nuclear symmetry energy as-20 MeV ≤ L ≤ 55 MeV with 68% confidence band using available measurements on charge radii. This is a moderately soft symmetry energy, in contrast to stiff and soft symmetry energy indicated by PREX-II and CREX measurements of neutron skin thickness in 208 P b and 48 Ca, respectively. Our result is also in agreement with celestial constraints obtained from observational data for neutron stars.

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We propose a high-statistics measurement of few body nuclear structure and short range correlations in quasi-elastic scattering at 6.6 GeV from 2 H, 3 He and 3 H targets in Hall B with the CLAS12 detector. We will measure absolute cross sections for (e, e p) and (e, e pN) quasi-elastic reaction channels up to a missing momentum pmiss ≈ 1 GeV/c over a wide range of Q 2 and xB and construct the isoscalar sum of 3 H and 3 He. We will compare (e, e p) cross sections to nuclear theory predictions using a wide variety of techniques and N N interactions in order to constrain the N N interaction at short distances. We will measure (e, e pN) quasi-elastic reaction cross sections and (e, e pN)/(e, e p) ratios to understand short range correlated (SRC) N N pairs in the simplest non-trivial system. 3 H and 3 He, being mirror nuclei, exploit the maximum available isospin asymmetry. They are light enough that their ground states are readily calculable, but they already exhibit complex nuclear behavior, including N N SRCs. We will also measure d(e, e p) in order to help theorists constrain non-quasielastic reaction mechanisms in order to better calculate reactions on A = 3 nuclei. Measuring all three few body nuclei together is critical, in order to understand and minimize different reaction effects, such as single charge exchange final state interactions, in order to test ground-state nuclear models. We will also measure the ratio of inclusive (e, e) quasi-elastic cross sections (integrated over xB) from 3 He and 3 H in order to extract the neutron magnetic form factor G n M at small and moderate values of Q 2. We will measure this at both 6.6 GeV and 2.2 GeV. Simulations and previous experience with CLAS12 show that we can obtain meaningful statistics with 55 days of beam time. We request 20 beam days each on 3 He and 3 H, and 10 beam days on 2 H at an incident beam energy of 6.6 GeV. We request an additional 5.5 days of beam time at 2.2 GeV to measure G n M at low Q 2. Our proposed measurements will significantly constrain nuclear models for few body nuclear dynamics and short range structure. Also, we will measure the behavior of the neutron magnetic form factor at low to moderate Q 2. This experiment will use the base equipment for CLAS12 and requires the construction of a new 3 H target. The JLab Target Group has a preliminary target design. The groups working on this experiment bring previous experience working with a 3 H target in Hall A.

Following the fragmentation of a 550 MeV/u primary beam of 58 Ni, time-and energy-correlated γ decays from isomeric states in neutron-deficient nuclei in the 1f 7/2 shell have been identified. using the GSI fragment separator in combination with the RISING Ge-detector array. The results on isomers in the mirror pairs 43 22 Ti 21 -43 21 Sc 22 (I π = 3/2 + and 19/2 -), 45 24 Cr 21 -45 21 Sc 24 (I π = 3/2 + ), and 45 23 V 22 -45 22 Ti 23 (I π = 3/2 -) are discussed in the framework of large scale pf and sdpf shell-model calculations, the former in conjunction with isospin symmetry breaking effects with emphasis on effective charges.

Cross sections for 147,149 Sm(p,n) 147,149 Eu and 147,149 Sm(p,γ) 148,150 Eu were measured using the activation method. The results are compared to the predictions of the Hauser-Feshbach statistical model. Different γ-ray strength functions have been tested against the experimental values. In the case of 150 Eu, in order to reproduce the experimental isomeric population cross sections, various scenarios for unknown branching ratios of certain discrete states have been discussed. The results provide constraints for the optical model parameters dedicated to this insufficiently known area of isotopes. Such cross sections for (p,γ) reactions at energies below the Coulomb barrier are valuable for p-process nucleosynthesis calculations.

In order to study the Gamow-Teller (GT) transitions from the T z = +2 nucleus 44 Ca to the T z = +1 nucleus 44 Sc, where T z is the z component of isospin T , we performed the (p, n)-type (3 He, t) charge-exchange (CE) reaction at 140 MeV/nucleon and the scattering angles 0 • and 2.5 •. An energy resolution of 28 keV, that was realized by applying matching techniques to the magnetic spectrometer system, allowed the study of fragmented states. The GT transition strengths, B(GT), were derived up to the excitation energy (E x) of 13.7 MeV assuming the proportionality between cross sections and B(GT) values. The total sum of B(GT) values in discrete states was 3.7, which was 31% of the sum-rule-limit value of 12. Shell model calculations using the GXPF1J interaction could reproduce the gross features of the experimental B(GT) distribution, but not the fragmentation of the strength. By introducing the concepts of isospin, properties of isospin analogous transitions and states were investigated. (i) Assuming isospin symmetry, the T z = +2 → +1 and T z = −2 → −1 mirror GT transitions should have the same properties, where the latter can be studied in the β decay of 44 Cr to 44 V. First, we confirmed that the β-decay half-life T 1/2 of 44 Cr can be reproduced using the B(GT) distribution from the 44 Ca(3 He, t) measurement. Then, the 0 • , (3 He, t) spectrum was modified to deduce the "β-decay spectrum" and it was compared with the delayed-proton spectrum from the 44 Cr β decay. The two spectra were mostly in agreement for the GT excitations, but suppression of the proton decay was found for the T = 2 isobaric analog state (IAS). (ii) Starting from the T = 2 ground state of 44 Ca, the (3 He, t) can excite GT states (state populated by GT transitions) with T = 1, 2, and 3. On the other hand, the 44 Ca(p, p) reaction can excite spin-M1 states (states populated by spin-M1 transitions) with T = 2 and 3 that are analogous to the T = 2 and 3 GT states, respectively. By comparing the spectra from these two reactions, a T value of 2 is suggested for several GT states in the E x = 11.5-13.7 MeV region. (iii) It has been suggested that the T = 2, J π = 0 + double isobaric analog state (DIAS) at 9.338 MeV in the T z = 0 nucleus 44 Ti forms an isospin-mixed doublet with a subsidiary 0 + state at 9.298 MeV. Since no corresponding state was found in the T z = +1 nucleus 44 Sc, we suggest T = 0 for the subsidiary state.

The unbound proton-rich nuclei 16 F and 15 F are investigated experimentally and theoretically. Several experiments using the resonant elastic scattering method were performed at GANIL with radioactive beams to determine the properties of the low lying states of these nuclei. Strong asymmetry between 16 F-16 N and 15 F-15 C mirror nuclei is observed. The strength of the nucleon − nucleon effective interaction involving the loosely bound proton in the s 1/2 orbit is significantly modified with respect to their mirror nuclei 16 N and 15 C. The reduction of the effective interaction is estimated by calculating the interaction energies with a schematic zero-range force. It is found that, after correcting for the effects due to changes in the radial distribution of the single-particle wave functions, the mirror symmetry of the a e-mail:

Excited states in 46 Cr were sought using the 12 C(36 Ar,2n) reaction. Gamma rays were detected with the Gammasphere array, and the Z value of the reaction products was determined with an ionization chamber located at the focal plane of the Fragment Mass Analyzer. In addition to the ground-state band observed up to I π = 10 + (tentatively 12 +), five states are proposed to belong to the 3 − band. The mirror energy differences with the analog states in 46 Ti present a pronounced staggering effect between the odd and even spin members that is reproduced well by shell-model calculations incorporating the different Coulomb contributions, monopole, multipole, and single-particle effects together with an isospin-nonconserving interaction that accounts for the so-called J = 2 anomaly. Dramatically different E1 decay patterns for members of the 3 − band between the 46 Cr and 46 Ti mirrors are also observed.

The deduction of 4 coefficients of the semi-empirical mass formula is presented as a function with two constants of proportionality: which relates the energy of the nuclear volume with volume and which relates volume with the mass number. Next the development of a proprietary method is presented-one that permits the simultaneous calculation of 4 of the 5 coefficients of the original semi-empirical formula. This method, which is direct and does not employ or require the use of successive approximations or iterations, is sufficiently didactic. It makes use of the experimental binding energies from 6 stable isotopes with a mass number odd-. Subsequently as validation, the coefficients are utilized for the theoretical calculation of the atomic masses of 237 stable isotopes and are compared with the experimental masses. Additionally, the calculation of the coefficients of proportionality and , the unit nuclear radius , the coefficients of nuclear surface tension , and the nuclear density are presented as well.

The deduction of 4 coefficients of the semi-empirical mass formula is presented as a function with two constants of proportionality: which relates the energy of the nuclear volume with volume and which relates volume with the mass number. Next the development of a proprietary method is presented-one that permits the simultaneous calculation of 4 of the 5 coefficients of the original semi-empirical formula. This method, which is direct and does not employ or require the use of successive approximations or iterations, is sufficiently didactic. It makes use of the experimental binding energies from 6 stable isotopes with a mass number odd-. Subsequently as validation, the coefficients are utilized for the theoretical calculation of the atomic masses of 237 stable isotopes and are compared with the experimental masses. Additionally, the calculation of the coefficients of proportionality and , the unit nuclear radius , the coefficients of nuclear surface tension , and the nuclear density are presented as well.

Isospin symmetry is expected for the T z 1 ! 0 isobaric analogous transitions in isobars with mass number A, where T z is the z component of isospin T. Assuming this symmetry, strengths of analogous Gamow-Teller (GT) transitions within A 50 isobars were determined from a high energy-resolution T z 1 ! 0, 50 Cr 3 He; t 50 Mn study at 0 in combination with the decay Q value and lifetime from the T z ÿ1 ! 0, 50 Fe ! 50 Mn decay. This method can be applied to other pf-shell nuclei and can be used to study GT strengths of astrophysical interest.

A high energy-resolution 11 B͑ 3 He, t͒ 11 C experiment was performed at 0°and an intermediate incident energy of 140 MeV/ nucleon for the study of precise Gamow-Teller (GT) transition strengths. Two doublet states at Ϸ4.5 and Ϸ8.4 MeV were clearly resolved with a resolution of 45 keV. The strengths are compared with a calculation using an ab initio no-core shell model, which became available for the A = 11 system recently. It was found that a calculation including a three-nucleon interaction better reproduces the observed GT transition strengths.

The nuclear mass dependence of the number of short-range correlated (SRC) proton-proton (pp) and proton-neutron (pn) pairs in nuclei is a sensitive probe of the dynamics of short-range pairs in the ground state of atomic nuclei. This work presents an analysis of electroinduced single-proton and two-proton knockout measurements off 12 C, 27 Al, 56 Fe, and 208 Pb in kinematics dominated by scattering off SRC pairs. The nuclear mass dependence of the observed A(e, e pp)/ 12 C(e, e pp) cross-section ratios and the extracted number of pp-and pn-SRC pairs are much softer than the mass dependence of the total number of possible pairs. This is in agreement with a physical picture of SRC affecting predominantly nucleon-nucleon pairs in a nodeless relativeS state of the mean-field basis.

LBL-1957 The Droplet Model of nuclear masses and density distributions, introduced in Ref. [1] for spherical configurations, is generalized to arbitrary shapes. Equations in closed form are given for the neutron and proton density non-uniformities induced by the electric forces, and also for the dependence of the neutron skin thickness on position on the nuclear surface. The formulae for the corrections to the nuclear energy associated with these effects are derived and this leads to a Droplet Model atomic mass formula which is presented with a preliminary set of coefficients adjusted to nuclear ground state masses and fission barriers.

The Coulomb energy for different nuclear model with small computing effort and high accuracy is a great challenge in physics as well as in quantum chemistry research. In this work we applied a classical electrodynamics theory and derived a simple procedure and expression for calculating the Coulomb energy for atomic nuclei taking into consideration the finite size of protons. The corresponding results are compared with the direct Coulomb energy obtained from two-parameter Fermi distributions. The formula obtained, which varies directly to the proton number and varies inversely to the cube root of mass number, was applied and calculated numerically the values of Coulomb energy for light, medium and heavy nuclei. To examine the effect of finite size of proton on Coulomb energy, a graph of Coulomb energy as a function of proton number was presented. The results obtained showed that due to the finite size of proton, the values of the previously calculated values of the Coulomb energy are reduced by less than 2%. This is because the protonproton distance increased due to finite size effect of the proton and thus affects the magnitude of the Coulomb energy. This showed that calculation of Coulomb energy by taking into consideration, the finite size of proton leads to agreement with the experimental values. Thus, in studying the nuclear structure, it is very natural to assume the protons to be extended rather than point charges.

Studying weak nuclear responses, especially the Gamow-Teller (GT) transitions starting from stable as well as unstable nuclei, provide crucial and critical information on nuclear structure. Therefore, the study of GT transitions is a key issue in nuclear physics and also nuclear-astrophysics. Under the assumption of isospin symmetry, it is expected that the structure of mirror nuclei and the GT transitions starting from their ground states are identical. We have studied the corresponding GT transitions starting from T z = ±1 and ±2 pf-shell nuclei, respectively, by means of hadronic (3 He, t) charge-exchange reactions and mirror β decays. The results on GT strength distributions measured in β decays and (3 He, t) reactions performed at an intermediate incident energy of 140 MeV/nucleon and 0 • are compared. The combined results help provide an understanding of nuclear structure of nuclei far-from-stability.

When protons and neutrons (nucleons) are bound into atomic nuclei, they are close enough together to feel significant attraction, or repulsion, from the strong, short-distance part of the nucleon-nucleon interaction. These strong interactions lead to hard collisions between nucleons, generating pairs of highly-energetic nucleons referred to as short-range correlations (SRCs). SRCs are an important but relatively poorly understood part of nuclear structure 1-3 and mapping out the strength and isospin structure (neutron-proton vs proton-proton pairs) of these virtual excitations is thus critical input for modeling a range of nuclear, particle, and astrophysics measurements 3-5. Hitherto measurements used two-nucleon knockout or "triple-coincidence" reactions to measure the relative contribution of np-and pp-SRCs by knocking out a proton from the SRC and detecting its partner nucleon (proton or neutron). These measurements 6-8 show that SRCs are almost exclusively np pairs, but had limited statistics and required large model-dependent final-state interaction (FSI) corrections. We report on the first measurement using inclusive scattering from the mirror nuclei 3 H and 3 He to extract the np/pp ratio of SRCs in the A=3 system. We obtain a measure of the np/pp SRC ratio that is an order of magnitude more precise than previous experiments, and find a dramatic deviation from the near-total np dominance observed in heavy nuclei. This result implies an unexpected structure in the high-momentum wavefunction for 3 He and 3 H. Understanding these results will improve our understanding of the short-range part of the N-N interaction.

We propose a high-statistics measurement of few body nuclear structure and short range correlations in quasi-elastic scattering at 6.6 GeV from 2 H, 3 He and 3 H targets in Hall B with the CLAS12 detector. We will measure absolute cross sections for (e, e p) and (e, e pN) quasi-elastic reaction channels up to a missing momentum pmiss ≈ 1 GeV/c over a wide range of Q 2 and xB and construct the isoscalar sum of 3 H and 3 He. We will compare (e, e p) cross sections to nuclear theory predictions using a wide variety of techniques and N N interactions in order to constrain the N N interaction at short distances. We will measure (e, e pN) quasi-elastic reaction cross sections and (e, e pN)/(e, e p) ratios to understand short range correlated (SRC) N N pairs in the simplest non-trivial system. 3 H and 3 He, being mirror nuclei, exploit the maximum available isospin asymmetry. They are light enough that their ground states are readily calculable, but they already exhibit complex nuclear behavior, including N N SRCs. We will also measure d(e, e p) in order to help theorists constrain non-quasielastic reaction mechanisms in order to better calculate reactions on A = 3 nuclei. Measuring all three few body nuclei together is critical, in order to understand and minimize different reaction effects, such as single charge exchange final state interactions, in order to test ground-state nuclear models. We will also measure the ratio of inclusive (e, e) quasi-elastic cross sections (integrated over xB) from 3 He and 3 H in order to extract the neutron magnetic form factor G n M at small and moderate values of Q 2. We will measure this at both 6.6 GeV and 2.2 GeV. Simulations and previous experience with CLAS12 show that we can obtain meaningful statistics with 55 days of beam time. We request 20 beam days each on 3 He and 3 H, and 10 beam days on 2 H at an incident beam energy of 6.6 GeV. We request an additional 5.5 days of beam time at 2.2 GeV to measure G n M at low Q 2. Our proposed measurements will significantly constrain nuclear models for few body nuclear dynamics and short range structure. Also, we will measure the behavior of the neutron magnetic form factor at low to moderate Q 2. This experiment will use the base equipment for CLAS12 and requires the construction of a new 3 H target. The JLab Target Group has a preliminary target design. The groups working on this experiment bring previous experience working with a 3 H target in Hall A.

B =1.24 and Q 2 =2 (GeV/c) 2 are reported.The data are compared to Relativistic Distorted Wave Impulse Approximation (RDWIA) calculations for the 4 He(e; e'p) 3 H channel. Significantly more events in the narrow triton missing mass region that we used, 0.017 GeV ≤ Emiss ≤ 0.022 GeV, are measured for missing momenta pm ≥ 0:45 GeV/c than are predicted by the theoretical model. This narrow missing mass region was chosen to minimize (pnn) and (p,d) background bleeding into the (p,t) state in the theoretical model. These excess events suggest that the effects of initial-state multi-nucleon correlations are stronger than expected by the RDWIA model. The ratio of the experimental cross sections to the theory cross sections shows a smooth dependence with missing momentum except in the region where the proton's predicted momentum distribution has a deep minimum.

We propose a high-statistics measurement of few body nuclear structure and short range correlations in quasi-elastic scattering at 6.6 GeV from 2 H, 3 He and 3 H targets in Hall B with the CLAS12 detector. We will measure absolute cross sections for (e, e p) and (e, e pN) quasi-elastic reaction channels up to a missing momentum pmiss ≈ 1 GeV/c over a wide range of Q 2 and xB and construct the isoscalar sum of 3 H and 3 He. We will compare (e, e p) cross sections to nuclear theory predictions using a wide variety of techniques and N N interactions in order to constrain the N N interaction at short distances. We will measure (e, e pN) quasi-elastic reaction cross sections and (e, e pN)/(e, e p) ratios to understand short range correlated (SRC) N N pairs in the simplest non-trivial system. 3 H and 3 He, being mirror nuclei, exploit the maximum available isospin asymmetry. They are light enough that their ground states are readily calculable, but they already exhibit complex nuclear behavior, including N N SRCs. We will also measure d(e, e p) in order to help theorists constrain non-quasielastic reaction mechanisms in order to better calculate reactions on A = 3 nuclei. Measuring all three few body nuclei together is critical, in order to understand and minimize different reaction effects, such as single charge exchange final state interactions, in order to test ground-state nuclear models. We will also measure the ratio of inclusive (e, e) quasi-elastic cross sections (integrated over xB) from 3 He and 3 H in order to extract the neutron magnetic form factor G n M at small and moderate values of Q 2. We will measure this at both 6.6 GeV and 2.2 GeV. Simulations and previous experience with CLAS12 show that we can obtain meaningful statistics with 55 days of beam time. We request 20 beam days each on 3 He and 3 H, and 10 beam days on 2 H at an incident beam energy of 6.6 GeV. We request an additional 5.5 days of beam time at 2.2 GeV to measure G n M at low Q 2. Our proposed measurements will significantly constrain nuclear models for few body nuclear dynamics and short range structure. Also, we will measure the behavior of the neutron magnetic form factor at low to moderate Q 2. This experiment will use the base equipment for CLAS12 and requires the construction of a new 3 H target. The JLab Target Group has a preliminary target design. The groups working on this experiment bring previous experience working with a 3 H target in Hall A.

High-momentum configurations of nucleon pairs at short-distance are probed using measurements of the 12 C(e, e p) and 12 C(e, e pN) reactions (where N is either n or p), at high-Q 2 and xB > 1.1. The data span a missing-momentum range of 300-1000 MeV/c and are predominantly sensitive to the transition region of the strong nuclear interaction from a Tensor to Scalar interaction. The data are well reproduced by theoretical calculations using the Generalized Contact Formalism with both chiral and phenomenological nucleon-nucleon (N N) interaction models. This agreement suggests that the measured high missing-momentum protons up to 1000 MeV/c predominantly belong to short-ranged correlated (SRC) pairs. The measured 12 C(e, e pN) / 12 C(e, e p) and 12 C(e, e pp) / 12 C(e, e pn) cross-section ratios are consistent with a decrease in the fraction of proton-neutron SRC pairs and increase in the fraction of proton-proton SRC pairs with increasing missing momentum. This confirms the transition from an isospin-dependent tensor N N interaction at ∼ 400 MeV/c to an isospin-independent scalar interaction at high-momentum around ∼ 800 MeV/c as predicted by theoretical calculation.

The microscopic effective charges in mirror nuclei 51 Mn and 51 Fe are investigated with the particle-vibration coupling model based on the self-consistent Skyrme-Hartree-Fock and continuum random-phase-approximation approaches. The isovector parts are predicted to be around 0.15, and the proton effective charges are around 1.25 e, which is less than the empirical value of e eff p = 1.5 e. The microscopic effective charges in neutron rich 51 Mn are about 10% less than its proton rich mirror. These effective charges are combined with the shell model to calculate the reduced electric quadrupole transition probability B (E 2) values in 51 Mn and 51 Fe. It turns out that the microscopic effective charges have well reproduced the B (E 2) values and its ratio in the terminating states.

The unbound proton-rich nuclei 16 F and 15 F are investigated experimentally and theoretically. Several experiments using the resonant elastic scattering method were performed at GANIL with radioactive beams to determine the properties of the low lying states of these nuclei. Strong asymmetry between 16 F-16 N and 15 F-15 C mirror nuclei is observed. The strength of the nucleon − nucleon effective interaction involving the loosely bound proton in the s 1/2 orbit is significantly modified with respect to their mirror nuclei 16 N and 15 C. The reduction of the effective interaction is estimated by calculating the interaction energies with a schematic zero-range force. It is found that, after correcting for the effects due to changes in the radial distribution of the single-particle wave functions, the mirror symmetry of the a e-mail:

The first excited 2 + state of 36 Ca has been identified by its γ-decay, exploiting the two-step fragmentation technique at the FRS-RISING setup at GSI. This is the heaviest T z = −2 nucleus in the Segré chart in which a γ-decay of an excited state has been observed. A stable beam of 40 Ca at 420A MeV impinged on a primary 9 Be target. Out of the secondary beam of fragmentation products, 37 Ca was separated by the FRS and struck on a second 9 Be target at the final focus of the FRS. The energy for the 2 + 1 decay of 36 Ca was determined to be 3015(16) keV, which is 276 keV lower than in its T = 2 mirror 36 S. This mirror energy difference (MED) is discussed in the framework of shell model calculations using a 16 O core, the sd shell isospin symmetric interaction USD and experimental single-particle energies from 17 O and 17 F. The results show that the MED within the sd shell provide a sensitive test for the evolution of the N, Z = 14, 16 subshell gaps towards the driplines. Especially the N , Z = 16 gap is determined by Thomas-Ehrman shift in the A = 17, T = 1/2 isospin doublet, while Coulomb effects are found to have marginal influence.

Lifetime measurements in the mirror nuclei 47 Cr and 47 V were performed by means of the Doppler-shift attenuation method using the multidetector array EUROBALL, in conjunction with the ancillary detectors ISIS and the Neutron Wall. The determined transition strengths in the yrast cascades are well described by full pf shell model calculations.

Single-particle for the doubly magic nuclei 48 Ca and 48 Ni are calculated within the framework of the Green's function using the CD-Bonn, Argonne V18 and N 3 LO nucleon-nucleon interactions. Both the continuous and conventional choices of single particle energies are used. Additional binding energy is obtained from the using the continuous choice. We also compare the binding energies obtained in this study with those obtained by various authors employing different method and techniques. The results show good agreement between the Green function calculated values using conventional choice and the experimental values for 48 Ni and 48 Ca nuclei. Also we found that, the proton-rich nucleus 48 Ni is less tightly bound by approximately 1.0 MeV per nucleon than its mirror nucleus 48 Ca, and this result is in good agreement with theoretical mass table evaluations.

Binding energy differences of mirror nuclei for A=15, 17, 27, 29, 31, 33, 39 and 41 are calculated in the framework of relativistic deformed mean-field theory. The spatial components of the vector meson fields and the photon are fully taken into account in a self-consistent manner. The calculated binding energy differences are systematically smaller than the experimental values and lend support to the existency of the Okamoto-Nolen-Schiffer anomaly found decades ago in nonrelativistic calculations. For the majority of the nuclei studied, however, the results are such that the anomaly is significantly smaller than the one obtained within state-of-the-art nonrelativistic calculations.

We propose a high-statistics measurement of few body nuclear structure and short range correlations in quasi-elastic scattering at 6.6 GeV from 2 H, 3 He and 3 H targets in Hall B with the CLAS12 detector. We will measure absolute cross sections for (e, e p) and (e, e pN) quasi-elastic reaction channels up to a missing momentum pmiss ≈ 1 GeV/c over a wide range of Q 2 and xB and construct the isoscalar sum of 3 H and 3 He. We will compare (e, e p) cross sections to nuclear theory predictions using a wide variety of techniques and N N interactions in order to constrain the N N interaction at short distances. We will measure (e, e pN) quasi-elastic reaction cross sections and (e, e pN)/(e, e p) ratios to understand short range correlated (SRC) N N pairs in the simplest non-trivial system. 3 H and 3 He, being mirror nuclei, exploit the maximum available isospin asymmetry. They are light enough that their ground states are readily calculable, but they already exhibit complex nuclear behavior, including N N SRCs. We will also measure d(e, e p) in order to help theorists constrain non-quasielastic reaction mechanisms in order to better calculate reactions on A = 3 nuclei. Measuring all three few body nuclei together is critical, in order to understand and minimize different reaction effects, such as single charge exchange final state interactions, in order to test ground-state nuclear models. We will also measure the ratio of inclusive (e, e) quasi-elastic cross sections (integrated over xB) from 3 He and 3 H in order to extract the neutron magnetic form factor G n M at small and moderate values of Q 2. We will measure this at both 6.6 GeV and 2.2 GeV. Simulations and previous experience with CLAS12 show that we can obtain meaningful statistics with 55 days of beam time. We request 20 beam days each on 3 He and 3 H, and 10 beam days on 2 H at an incident beam energy of 6.6 GeV. We request an additional 5.5 days of beam time at 2.2 GeV to measure G n M at low Q 2. Our proposed measurements will significantly constrain nuclear models for few body nuclear dynamics and short range structure. Also, we will measure the behavior of the neutron magnetic form factor at low to moderate Q 2. This experiment will use the base equipment for CLAS12 and requires the construction of a new 3 H target. The JLab Target Group has a preliminary target design. The groups working on this experiment bring previous experience working with a 3 H target in Hall A.

Single-particle for the doubly magic nuclei 48 Ca and 48 Ni are calculated within the framework of the Green's function using the CD-Bonn, Argonne V18 and N 3 LO nucleon-nucleon interactions. Both the continuous and conventional choices of single particle energies are used. Additional binding energy is obtained from the using the continuous choice. We also compare the binding energies obtained in this study with those obtained by various authors employing different method and techniques. The results show good agreement between the Green function calculated values using conventional choice and the experimental values for 48 Ni and 48 Ca nuclei. Also we found that, the proton-rich nucleus 48 Ni is less tightly bound by approximately 1.0 MeV per nucleon than its mirror nucleus 48 Ca, and this result is in good agreement with theoretical mass table evaluations.

The neutron separation energy is the minimum energy required to remove a neutron from a nucleus. It is the difference between the rest mass energy of the nucleus with one less neutron and the actual rest mass energy of the nucleus. Considering Einstein's mass-energy equivalence relation and using the contributions of the liquid-drop model, we first analyze the various terms that build up the Bethe-von Weizsäcker formula. Using this, we estimate the binding energy of a nucleus which in-turn can be used to calculate the neutron separation energies. This was done to obtain the separation energies of different isotopes of Oxygen-8 and Nickel-28. Using the relationship between binding energy and separation energy, the single as well as double neutron separation energies for transition isotopes of Oxygen-8 and Nickel-28 were calculated. We then progressed on to investigate the co-relation of Separation Energies with the Q-Value for a nuclear reaction and discuss its possible consequences for stellar fusion process.

In high-resolution 42,44Ca(e,e') reactions, isovector M2 transition strengths to the ground-state analogues of 42,44K have been measured. A comparison with the analogous unique first-forbidden fl-decays shows that at the photon point these transitions arise mainly from spin magnetizations.

Excited states in the N = Z −2 nucleus 44 V have been observed for the first time. The states have been identified through particle-γ-γ coincidence relationships and comparison with analogue states in the mirror nucleus 44 Sc. Mirror energy differences have been extracted and compared to state-of-theart shell model calculations which include charge symmetry breaking forces. Observed decay pattern asymmetries between the mirror pair are discussed in terms of core excitations, electromagnetic spinorbit effects and isospin mixing.

The Coulomb energy for different nuclear model with small computing effort and high accuracy is a great challenge in physics as well as in quantum chemistry research. In this work we applied a classical electrodynamics theory and derived a simple procedure and expression for calculating the Coulomb energy for atomic nuclei taking into consideration the finite size of protons. The corresponding results are compared with the direct Coulomb energy obtained from two-parameter Fermi distributions. The formula obtained, which varies directly to the proton number and varies inversely to the cube root of mass number, was applied and calculated numerically the values of Coulomb energy for light, medium and heavy nuclei. To examine the effect of finite size of proton on Coulomb energy, a graph of Coulomb energy as a function of proton number was presented. The results obtained showed that due to the finite size of proton, the values of the previously calculated values of the Coulomb energy are reduced by less than 2%. This is because the protonproton distance increased due to finite size effect of the proton and thus affects the magnitude of the Coulomb energy. This showed that calculation of Coulomb energy by taking into consideration, the finite size of proton leads to agreement with the experimental values. Thus, in studying the nuclear structure, it is very natural to assume the protons to be extended rather than point charges.

Gamow-Teller (GT) transitions are the most common weak-interaction processes in the Universe. They play important roles in various processes of nucleosynthesis, for example, in the rapid proton-capture process (rp-process). In the pf-shell region, the rp-process runs through neutrondeficient nuclei with T z = −2, −1, and 0 mainly by means of GT and Fermi transitions, where T z is the z component of isospin T defined by T z = (N − Z)/2. Under the assumption of isospin symmetry, mirror nuclei with reversed Z and N numbers, and thus with opposite signs of T z , have the same structure. Therefore, symmetry is also expected for the GT transitions starting from and ending up in mirror nuclei. We have been studying the T z = −2 → −1 and −1 → 0 GT transitions in β decays, while those from stable T z = +2 and +1 nuclei by means of hadronic (3 He, t) charge-exchange (CE) reactions. The results from these studies are compared in order to examine the mirror-symmetry structure in nuclei. In addition, these results are combined for the better understanding of GT transitions in the pf-shell region.

The tin isotope 100Sn is of singular interest for nuclear structure due to its closed-shell proton and neutron configurations. It is also the heaviest nucleus comprising protons and neutrons in equal numbers—a feature that enhances the contribution of the short-range proton–neutron pairing interaction and strongly influences its decay via the weak interaction. Decay studies in the region of 100Sn have attempted to prove its doubly magic character1 but few have studied it from an ab initio theoretical perspective2,3, and none of these has addressed the odd-proton neighbours, which are inherently more difficult to describe but crucial for a complete test of nuclear forces. Here we present direct mass measurements of the exotic odd-proton nuclide 100In, the beta-decay daughter of 100Sn, and of 99In, with one proton less than 100Sn. We use advanced mass spectrometry techniques to measure 99In, which is produced at a rate of only a few ions per second, and to resolve the ground and isome...

A phenomenological Coulomb energy equation has been derived for spherical nuclei with diffuse surfaces. Contributions from the direct and exchange Coulomb energy and from the electromagnetic spin-orbit interaction are included explicitly. The experimental Coulomb displacement energies of 42 essentially spherical nuclei with 2 2 28 have been subjected to a least-squares analysis with the shape parameters of the ground state charge distributions required to agree with those obtained from electron scattering and muon capture X-ray experiments. Agreement between the experimental and calculated energies with a standard deviation of about 20 keV is obtained if (i) the ratio between the rms radii of the neutron excess and the proton core is taken between about 1.10 and 1.15, (ii) a smoothly A-dependent correction term which varies between about +450 keV in the light nuclei and +350 keV in the heavy nuclei is introduced, and (iii) an averaged contribution from the electromagnetic spin-orbit interaction is used rather than the expected shell-mode1 contribution. Justification for this averaging may be provided by amounts of not less than 15 % of excitations into higher shellmodel orbits for all nuclei. The Coulomb displacement energies of vibrational and rotational nuclei are observed to be smaller by up to 200 keV than corresponding spherical nuclei. Neutron halos have been calculated and are found to be in very good agreement with the results of Hartree-Fock calculations, the droplet mode1 of Myers and Swiatecki and the calculations by Nolen and Schiffer using wave functions generated in a Woods-Saxon potential well. The calculated neutron halo for zo8Pb is 0.25kO.05 fm.

The exotic structures in the 2s 1/2 states of five pairs of mirror nuclei 17 O-17 F, 26 Na-26 P, 27 Mg-27 P, 28 Al-28 P and 29 Si-29 P are investigated with the relativistic mean-field (RMF) theory and the singleparticle model (SPM) to explore the role of the Coulomb effects on the proton halo formation. The present RMF calculations show that the exotic structure of the valence proton is more obvious than that of the valence neutron of its mirror nucleus, the difference of exotic size between each mirror nuclei becomes smaller with the increase of mass number A of the mirror nuclei and the ratios of the valence proton and valence neutron root-mean-square (RMS) radius to the matter radius in each pair of mirror nuclei all decrease linearly with the increase of A. In order to interpret these results, we analyze two opposite effects of Coulomb interaction on the exotic structure formation with SPM and find that the contribution of the energy level shift is more important than that of the Coulomb barrier for light nuclei. However, the hindrance of the Coulomb barrier becomes more obvious with the increase of A. When A is larger than 34, Coulomb effects on the exotic structure formation will almost become zero because its two effects counteract with each other.

With a high energy-resolution of E = 21 keV in the 34 S(3 He, t) 34 Cl measurement at 0 • and at 140 MeV/nucleon, strengths of Fermi and Gamow-Teller (GT) transitions between T z = +1 and T z = 0 states were studied, where T z is the z component of isospin T. The corresponding isospin-symmetric transitions connecting T z = −1 and T z = 0 states can be studied in the 34 Ar β + decay. The strengths of corresponding GT transitions were compared up to the excitation energy (E x) of 3.1 MeV. A good agreement was observed for the two strong transitions to states around E x = 3 MeV, while a disagreement of 40% was observed for a weaker transition to a low-lying state.

The structure of 17 C is used to define a nuclear interaction that, when used in a multichannel algebraic scattering theory for the n+ 16 C system, gives a credible definition of the (compound) excitation spectra. When couplings to the low-lying collective excitations of the 16 C-core are taken into account, both sub-threshold and resonant states about the n+ 16 C threshold are found. Adding Coulomb potentials to that nuclear interaction, the method is used for the mirror system of p+ 16 Ne to specify the low-excitation spectrum of the particle unstable 17 Na. We compare the results with those of a microscopic cluster model. A spectrum of low excitation resonant states in 17 Na is found with some differences to that given by the microscopic-cluster model. The calculated resonance half-widths (for proton emission) range from ∼ 2 to ∼ 672 keV.

We propose a high-statistics measurement of few body nuclear structure and short range correlations in quasi-elastic scattering at 6.6 GeV from $^2$H, $^3$He and $^3$H targets in Hall B with the CLAS12 detector. We will measure absolute cross sections for $(e,e'p)$ and $(e,e'pN)$ quasi-elastic reaction channels up to a missing momentum $p_{miss} \approx 1$ GeV/c over a wide range of $Q^2$ and $x_B$ and construct the isoscalar sum of $^3$H and $^3$He. We will compare $(e,e'p)$ cross sections to nuclear theory predictions using a wide variety of techniques and $NN$ interactions in order to constrain the $NN$ interaction at short distances. We will measure $(e,e'pN)$ quasi-elastic reaction cross sections and $(e,e'pN)/(e,e'p)$ ratios to understand short range correlated (SRC) $NN$ pairs in the simplest non-trivial system. $^3$H and $^3$He, being mirror nuclei, exploit the maximum available isospin asymmetry. They are light enough that their ground states are rea...

The Coulomb energy for different nuclear model with small computing effort and high accuracy is a great challenge in physics as well as in quantum chemistry research. In this work we applied a classical electrodynamics theory and derived a simple procedure and expression for calculating the Coulomb energy for atomic nuclei taking into consideration the finite size of protons. The corresponding results are compared with the direct Coulomb energy obtained from two-parameter Fermi distributions. The formula obtained, which varies directly to the proton number and varies inversely to the cube root of mass number, was applied and calculated numerically the values of Coulomb energy for light, medium and heavy nuclei. To examine the effect of finite size of proton on Coulomb energy, a graph of Coulomb energy as a function of proton number was presented. The results obtained showed that due to the finite size of proton, the values of the previously calculated values of the Coulomb energy are reduced by less than 2%. This is because the proton-proton distance increased due to finite size effect of the proton and thus affects the magnitude of the Coulomb energy. This showed that calculation of Coulomb energy by taking into consideration, the finite size of proton leads to agreement with the experimental values. Thus, in studying the nuclear structure, it is very natural to assume the protons to be extended rather than point charges.

In this study the values of the β + disintegration energy is calculated using the standard values of masses of mirror nuclei. These values are used to plot a graph of β + transformation energy against A 2/3. The nuclear radius parameter is determined from the slop of the graph as r0 = 1.23 × 10-15 m. The study then continues to compute the numerical values of the Coulomb energy difference between mirror nuclei using Bethe-Weizsäcker mass formula. The nuclear radius parameter determined from the Coulomb energy difference appears to have a mean value of r0 = 1.2368 × 10-15 m. These calculated values are in good agreement with r0 = 1.2 × 10-15 m, measured from the experimental data by electron scattering and μ-mesonic atoms. These results have shown that the apparent discrepancy between the values for the nuclear charge parameter derived from electron scattering and μ-mesonic atoms and those derived from mirror nuclei experiments might not be attributed to the use of classical principles. Thus, these developments in the theoretical measurement for nuclear radius parameter from Coulomb energy difference and β + disintegration energy provide more accurate results which can be used to improve model parameters.