Supersoft Core Potentials Research Articles

Nuclear ground-state properties and nuclear forces in the unitary-model-operator approach: Application to 16O.

A formulation is given to derive an effective interaction in the framework of the unitary-model-operator approach. A unitary transformation is introduced to describe two-body correlations and is determined from the condition that the effective interaction should be decoupled between the low- and high-momentum spaces. A unitary transformation of the Hamiltonian is made and the transformed Hamiltonian is represented in a cluster-expansion form. The effective interaction thus defined is E independent and Hermitian. The contributions of one-, two-, and three-body-cluster terms are taken into consideration. The self-consistent single-particle potential is considered sym- metrically for both occupied (hole) and unoccupied (particle) states. The theory is applied to the calculation of the ground-state properties of $^{16}\mathrm{O}$ using three potentials, namely, the Paris, Reid soft-core, and supersoft-core potentials. A large gain in the binding energy is obtained. Final results for the gound-state energy and the charge radius are as follows: -119.2 MeV and 2.62 fm for the Paris, -115.1 MeV and 2.60 fm for the Reid soft core, and -121.7 MeV and 2.62 fm for the supersoft core. The single-particle energies of the occupied orbits are also calculated. Good agreement between the calculated and experimental energies is obtained. In particular, a large spin-orbit splitting of the 0p orbits is reproduced with the results 5.6 MeV for the Paris, 5.1 MeV for the Reid soft core, and 5.4 MeV for the supersoft core, which should be compared with the experimental value 6.1 MeV.

Nuclear matter calculations with isobar degrees of freedom for the Paris potential and isobar self-energy

A coupled channel calculation, with the compensated Paris potential and the isobar transition potential due to Green, Niskanen and Sainio, yields the nucleon and isobar self energies in nuclear matter. Unlike the Reid soft core, the Paris potential is found to bind the isobar at a small momentum by a potential of the order of 10 MeV. For a super soft core potential, the inclusion of isobar degrees of freedom produces a small change in binding energy in nuclear matter. In the present paper we find that for the momentum dependent Paris potential the change is even smaller when all self energies are calculated self-consistently. This is gratifying since the pion nucleon dynamics put into the derivation of the potential already contains isobar effects.

The four-nucleon problem with local realistic nn interactions

The ground state and the first excited 0 + state binding energies of the 4He are calculated within the framework of the hyperspherical method for the Gogny-Pirès-de Tourreil potential (GPDT), and for the two super soft core potentials (SSC.B and SSC.C) constructed by de Tourreil and Sprung. With neglect of the Coulomb effect, the ground state energies are found to be −30.10 MeV for GPDT, −25.88 MeV for SSC.B and −21.19 MeV for SSC.C. For the two first potentials we find an excited 0 + state. The location of this state above the ground state is found to be 25.66 MeV for GPDT and 25.11 MeV for SSC.B. We analyse the convergence of the ground state eigenvalues versus the grand orbital ( L = 2 K) in comparing the results of the coupled equation calculations (CE) with those of different approximations giving: a lower bound with the extreme adiabatic approximation (EAA), an upper bound with the uncoupled adiabatic approximation (UAA) and an accurate bound with the coupled adiabatic approximation (CAA).

γ(d,n)preaction with polarized and unpolarized gamma rays

The asymmetry function for the $\ensuremath{\gamma}(d,n)p$ reaction is calculated for the Paris and supersoft core potentials for gamma-ray energies, ${E}_{\ensuremath{\gamma}}$, extending from 20 to 150 MeV, at center of mass angles 45\ifmmode^\circ\else\textdegree\fi{}, 90\ifmmode^\circ\else\textdegree\fi{}, and 135\ifmmode^\circ\else\textdegree\fi{}. The relative photoneutron yield at ${E}_{\ensuremath{\gamma}}=20$ MeV is also calculated. In addition, the differential cross section, total cross section, and polarization of the outgoing protons are reported. The Paris potential gives good agreement with the experimental data for the differential and total cross sections. However, the discrepancy at 0\ifmmode^\circ\else\textdegree\fi{} still remains. It is found that the asymmetry function cannot be used to distinguish between the various nucleon-nucleon potentials.NUCLEAR REACTIONS $\ensuremath{\gamma}(d,n)p$. Calculated asymmetry function; total and differential cross sections.

Deuteron photoabsorption sum rule: Two-body effects

In deuteron photoabsorption, the effect of mesonic exchange currents is considered in detail. Related to the electric dipole operator D1 (Siegert form) and to the nuclear interactions, a factor k appears in the integrated cross-section σ0, previously obtained by the Thomas–Reiche–Kuhn dipole sum rule. The introduction of the two-body density [Formula: see text] modifies the form of D1 and increases κ which becomes κ + Δκ. The influence of several NN potentials is clearly shown on the factor Δκ, some 25% difference occurring between a super soft core potential and the Paris potential. In this last case the value of Δκ is about 50% of the initial κ value.

Analyses of the energy-dependent single-separable-potential models for the $$\mathcal{N}\mathcal{N}$$ scattering

By starting from a systematic study of the salient features regarding the quantum-mechanical two-particle scattering off an energy-dependent (ED) single separable potential and its connection with the rank-2 energy-independent (EI) separable potential in theT-(K-) amplitude formulation, the present status of the ED single-separable-potential models due to Tabakin (M1), Garcilazo (M2) and Ahmad (M3) has been discussed. It turned out that the incorporation of a self-consistent optimization procedure improves considerably the results of the1S0 and3S1 scattering phase shifts for the models (M2) and (M3) up to the c.m. wave numberq=2.5 fm−1, although the extrapolation of the results up toq=10 fm−1 reveals that the two models follow the typical behaviour of the well-known supersoft-core potentials. It has been found that a variant of (M3)—i.e. (M4) involving one more parameter—gives phase-shift results which are generally in excellent agreement with the data up toq=2.5 fm−1 and the extrapolation of the results for the1S0 case in the higher wave number range not only follows the corresponding data qualitatively, but also reflects a behaviour similar to the Reid soft-core and Hamada-Johnston potentials together with a good agreement with the recent [4/3] Pade fits. A brief discussion regarding the features resulting from the variations in the ED parts of all the four models under consideration and their correlations with the inverse-scattering theory methodology concludes the paper.

Nuclear matter calculation with a super soft core potential including isobar degrees of freedom

A complete nuclear matter calculation in lowest order Brueckner theory is done for a super soft core nucleon–nucleon potential due to de Tourreil, Rouben, and Sprung and the effect of including isobar degrees of freedom on binding energy, saturation, and half-shell G-matrices is considered in the frame work of the coupled channel formalism. The singlet and triplet S-state effective interaction is derived and its density and momentum dependence is studied. Comparison is made with the results obtained from the Reid soft core potential.

Photodisintegration of the deuteron employing a supersoft core potential

Employing the supersoft core potentials of deTourreil and Sprung, the differential cross section and polarization of the outgoing protons in the photodisintegration of the deuteron have been investigated for laboratory gamma-ray energies ranging from 10 to 150 MeV. The supersoft core potentials are found to give an appreciable decrease in the total cross section for the higher gamma-ray energies than when the Hamada-Johnston potential is used. These reductions in total cross section at higher energies are comparable with the increase obtained on including the effects of isobar configurations and meson exchange currents. The proton polarization is noticeably affected in $0\ifmmode^\circ\else\textdegree\fi{}<{\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}<60\ifmmode^\circ\else\textdegree\fi{}$ at ${E}_{\ensuremath{\gamma}}^{\mathrm{lab}}=150$ MeV.NUCLEAR REACTIONS $^{2}\mathrm{H}(\ensuremath{\gamma},n)p$. Supersoft core potentials.

One-hole states in double magic nuclei

We discuss the equation of motion $〈{\ensuremath{\psi}}_{\stackrel{^}{B}}|[H,{a}_{\ensuremath{\alpha}}]|{\ensuremath{\psi}}_{0}〉=({E}_{\stackrel{^}{B}}\ensuremath{-}{E}_{0}) 〈{\ensuremath{\psi}}_{\stackrel{^}{B}}|{a}_{\ensuremath{\alpha}}|{\ensuremath{\psi}}_{0}〉$ in the subspace of states $|{\ensuremath{\psi}}_{\stackrel{^}{B}}〉=\ensuremath{\Sigma}{\ensuremath{\alpha}}^{}{\ensuremath{\beta}}_{\ensuremath{\alpha}}{a}_{\ensuremath{\alpha}}|{\ensuremath{\psi}}_{0}〉$, where $|{\ensuremath{\psi}}_{0}〉$ is the correlated ground state of a double magic nucleus. It is shown that this equation can be solved with high accuracy if some low-order correlation functions of the $\mathrm{exp}S$ theory are known. Preliminary results are given for $^{3}\mathrm{H}$ and $^{15}\mathrm{N}$ for four different nucleon-nucleon interactions, i.e., the Reid-soft-core potential with and without the three-body correction of Blatt and McKellar, the Hamada-Johnston potential, and the de Toureill-Sprung supersoft-core potential. The connection with shell model states is discussed.NUCLEAR STRUCTURE $^{3}\mathrm{H}$, $^{15}\mathrm{N}$, $^{15}\mathrm{O}$ calculated hole states $^{4}\mathrm{He}$, $^{16}\mathrm{O}$. Centroid energies from microscopic theory.

Structure calculations for40Ca with the supersoft-core potential

The ground-state properties of40Ca are studied by using the Hartree-Fock approximation and an effective interaction calculated by means of the supersoft-core potential. Shell model spaces of various sizes are used. The effective interaction matrix elements used in the Hartree-Fock procedure, the ground-state binding energy and the r.m.s. radius obtained with the supersoft-core potential are compared with the results obtained with realistic hard-core potentials.

Theoretical investigation of the photodisintegration of deuteron at 0° for the outgoing protons

The serious discrepancy between the measurements of Hughes, Zieger, Wäffler, and Ziegler and published calculations for the differential cross section for the photodisintegration of the deuteron at 0° for the outgoing protons is found to be greatly reduced when calculations with supersoft core potentials are carried out. The measurements seem to favor a lower percentage of the ‘D’ state of the deuteron.

Generalized BCS calculations for the2s−1dshell with realistic interactions

Based on the Hartree-Fock calculations reported earlier, the ground-state properties of N = Z even-even nuclei in the 2s-1d shell are investigated within the generalized BCS approach employing T = 1, T = 0, and T = 1 + T = 0 pairing correlations and the modified Yale and supersoft core potentials. Comparisons are made with similar less sophisticated calculations reported earlier for the same nuclei using the Yale potential.

Axial symmetry ofMg24andS32in the BCS approximation

Employing the modified Yale and supersoft core potentials, BCS calculations are carried out for the ground-state properties of $^{24}\mathrm{Mg}$ and $^{32}\mathrm{S}$. It is found that the $T=0$ neutron-proton pairing correlations under the axially symmetric shape are more energetically favorable for $^{32}\mathrm{S}$, and equally favorable for $^{24}\mathrm{Mg}$, than the asymmetric shape obtained through the Hartree-Fock procedure. Comparisons are made with BCS results obtained via the Yale potential using the same shell-model expansion basis.

N=Zeven-even nuclei in the2s−1dshell

The ground-state properties of $N=Z$ even-even $2s\ensuremath{-}1d$ shell nuclei are studied within the framework of the Hartree-Fock approximation employing the modified Yale potential and the supersoft core potential. Shell-model spaces of various sizes are used. The results are compared with similar but less sophisticated calculations published earlier.NUCLEAR STRUCTURE $^{16}\mathrm{O}$, $^{20}\mathrm{Ne}$, $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, $^{32}\mathrm{S}$, $^{36}\mathrm{A}$, $^{40}\mathrm{Ca}$; Hartree-Fock method with various shell-model spaces. Modified Yale and supersoft core interactions.

The electric 3H and 3He formfactors for realistic potentials

Electric 3H and 3He formfactors for the Reid, Bressel-Kerman-Rouben and super soft-core potentials have been calculated with the hyperspherical function method.

Calculation of 3H, 3He properties with realistic NN-potentials in the hyperspherical basis

3H and 3He properties (the bound energy, the charge radius, S', P and D component weights and others) have been calculated using the Reid, Bressel-Kerman-Rouben and supersoft-core potentials.