The nucleon momentum and density distribution of the 4He nucleus using the Morse potential

The nucleon momentum and density distribution of the 4He nucleus are calculated by using the Morse single-particle potential. The parameters for the momentum distribution n(fc) are determined by fitting either the charge form factor to the available experimental data of the elastic electron scattering by 4He or the momentum distribution to the corresponding "experimental" values. The calculations can be performed partly analytically and the results show a considerable overall improvement with respect to those obtained with the oscillator shell model. The r.m.s radius of the charge density distribution determined by fitting the charge form factor is in very good agreement with the vaiues obtained by means of model independent analysis.

The form factor and the density distribution of the 4He nucleus using the Morse potential

The form factor and the density distribution of the He nucleus are calculated approximately using the Morse single-particle potential. The parameters are determined by fitting the theoretical charge form factor to the corresponding experimental data of the elastic electron scattering by 4He, which are extended to large values of the momentum transfer. The corrections due to the center of mass motion (in the fixed center of mass approach) and of the finite proton size have been taken into account. The calculations can be performed partly analytically and the results show a considerable im- provement with respect to those obtained with the oscillator shell model.

DEBYE-WALLER TYPE EXPRESSIONS FOR THE NUCLEAR ELASTIC FORM FACTORS AT SMALL MOMENTUM TRANSFERS

The problem of the estimate of the nuclear elastic form factors in Born approximation is discussed in the region of small momentum transfers q. It is shown that approximate expressions of the Debye-Waller type are suitable for estimates of these form-factors in the oscillator shell model, for sufficiently small q.

NUCLEAR MOMENTUM DISTRIBUTION WITH FRACTIONAL OCCUPATION PROBABILITIES OF THE SURFACE ORBITS

Simplified expressions for calculating nucléon momentum distributions are derived in the context of the harmonic oscillator shell model and in its modification in which fractional occupation probabilities of the surface orbits are used. The method is applied to study the proton momentum distribution of the spherical nucleus 40Ca. The values of the partial occupation probabilities used had been previously determined by fitting to the experimental elastic form factor data.

Nuclear distributions, rms radii and form factors with the harmonic oscillator shell model

General expressions for calculating nuclear distributions (proton, charge, matter and momentum), mean radii and nuclear form factors are derived by extending recent related works. They are based either on the simple harmonic oscillator shell model or on its modification in which fractional occupation probabilities of the surface orbits are used to fit the experimental elastic electron scattering data. The 40Ca and the values of partial occupation method is applied to the spherical nucleus probabilities are compared with those determined from experimental reaction data.

Shell-model calculations for upper pf-shell nuclei with an effective interaction

Results obtained for the energy spectra and the low-lying positive-parity energy eigenstates of the upper p f -shell nuclei 64Ge and 68Se with the use of the effective interaction JUN45 are reported. We address the question of how appropriate is the possibility to construct a symmetry-adapted shell model in a single oscillator shell using a Pairing-plus-Quadrupole Hamiltonian. Specifically, we study the goodness of the symmetries pseudo SU(3) and O(6) in the structure of the energy eigenstates. Finally, we relate our results to a proposed mixed-symmetry approach which is able to simultaneously account for the presence of both the pairing and the quadrupole modes as the most important ingredients in the effective interaction while using a restricted part of the full model space.

THE RESPONSE FUNCTION OF THE 4He, 16O AND 40Ca NUCLEI IN THE HARMONIC OSCILLATOR SHELL MODEL AND THE IMPULSE APPROXIMATIONS

In this work, the response functions (RFs) of the 4 He , 16 O and 40 Ca nuclei are calculated in the harmonic oscillator shell model (HOSM) and the impulse approximation (IA). First, the one-body momentum distribution and the one-body spectral functions for these nuclei are written in the HOSM configuration. Then, their RFs are calculated, in the two frameworks, namely the spectral and the momentum distribution functions, within the IA. Unlike our previous work, no further assumption is made to reduce the analytical complications. For each nucleus, it is shown that the (RF) evaluated using the corresponding spectral function has a sizable shift, with respect to the one calculated in terms of the momentum distribution function. It is concluded that for the heavier nuclei, this shift increases and reaches nearly to a constant value (approximately 62 MeV), i.e., similar to that of nuclear matter. It is discussed that in the nuclei with the few nucleons, the above shift can approximately be ignored. This result reduces the theoretical complication for the explanation of the ongoing deep inelastic scattering (DIS) experiments of 3 H or 3 H nucleus target in the Jefferson Laboratory. On the other hand, it is observed that in the heavier nuclei, the RF heights (width) decrease (increase), i.e., the comparison between the theoretical and the experimental electron nucleus scattering cross-section is more sensible for heavy nuclei rather than the light ones.

THE SHELL MODEL AND THE IMPULSE APPROXIMATIONS APPROACH TO THE RESPONSE FUNCTION OF 4He, 16O AND 40Ca NUCLEI

The ambiguities proposed by Benhar et al., about the the different implementation of the impulse approximation for calculating the response function of many-fermion systems, are investigated theoretically in the frame work of simple harmonic oscillator shell model for the double closed shell nuclei, e.g. 4 He , 16 O and 40 Ca nuclei. For each nucleus as a finite system, we evaluate the response function by using its definition in terms of the one-body spectral function and the one-body momentum distribution. It is demonstrated analytically, that there exists a sizable shift between the two schemes for each nucleus, which increases as we switch to the heavier nuclei. So one can conclude that for the nuclei with atomic number less than 4, such as 2 H , 3 H or 3 He , it is good approximation to ignore this discrepancy. This conclusion is important for theoretical explanation of the ongoing deep inelastic scattering (DIS) experiments of 3 H or 3 H in the Jefferson Laboratory. However present calculation confirms the work of Modarres and Younesizadeh (2010), in which they have shown that, the above shift can be removed by imposing the impulse approximation in the same footing in the many-fermion wave-function.

EXTENDED MICROSCOPIC CLUSTER MODEL STUDY OF FOUR NUCLEON SCATTERING

d+d ( S -wave) elastic scattering phase shifts are studied in an extended microscopic cluster model in order to investigate cluster-breaking effects appearing in the low-energy scattering. The description of the cluster wave function is extended from a simple (0s) harmonic-oscillator shell model to a few-body model, in which the wave function of the sub-system is determined with the Stochastic Variational Method (SVM). To compare the cluster breaking effects with realistic and effective interactions, we employed the G3RS potential as a realistic interaction and the Minnesota (MN) potential as an effective interaction. The calculated phase shifts show that t+p and 3 He +n channels are strongly coupled to the d+d channel for the case of the realistic interaction (G3RS). On the contrary, the coupling of these channels plays a relatively minor role for the case of the effective interaction (MN).