Characteristics of scattering of Λ hyperons from nuclei within the potential model

The characteristics of bound states of hypernuclei were calculated in [1] in a wide range of mass numbers within the potential model for three different potentials. In this study, the phase shifts and low-energy parameters for scattering of Λ hyperons from core nuclei, considered in [1], have been calculated for the same potentials. The calculated scattering lengths and effective radii are compared with their values found in [1] on the basis of the data on the binding energies and vertex constants of hypernuclei.     

Hyperon properties in finite nuclei using realistic YN interactions

Single-particle energies of Λ and Σ hyperons in several nuclei are obtained from the relevant self-energies. The latter are constructed within the framework of a perturbative many-body approach employing present realistic hyperon-nucleon interactions such as the models of the Jülich and Nijmegen groups. The effects of the non-locality and energy dependence of the self-energy on the bound states are investigated. It is also shown that, although the single-particle hyperon energies are well reproduced by local Woods-Saxon hyperon-nucleus potentials, the wave functions from the non-local self-energy are far more extended. Implications of this behavior for the mesonic weak decay of Λ hypernuclei are discussed.     

Characteristics of the discrete and continuous spectra of the <Superscript>4</Superscript>He + Λ system

In view of projected experiments on the production of relativistic hypernuclei and the investigation of reactions induced by them, the characteristics of the hypernucleus and low-energy parameters of the _Λ ⁵ He hyperon scattering from ⁴He were calculated. The interaction of the Λ hyperon and the α particle is described by the effective Λα potential in two different forms. The root-mean-square radius of the Λ hyperon in the _Λ ⁵ He hypernucleus, the vertex constant for the _Λ ⁵ He ? ⁴He + Λ process, and the corresponding asymptotic normalization coefficient of the _Λ ⁵ He wave function were calculated by solving the radial Schrödinger equation. The scattering length and the effective radius for the scattering of Λ from ⁴He were calculated by two methods. The calculated characteristics turn out to be sensitive to the form of the Λα potential.     

Calculating the characteristics of neutron-deuteron and proton-deuteron systems in a two-body potential model

³H and ³He nuclei are considered in a two-body model (³H = n + d; ³He = p + d). Two independent approaches are used: in the first, interaction is described by the folding potential, while NN potentials are taken in the Hulthen form with allowance for violations of isotopic invariance. The second approach features phenomenological Hulthen and Yukawa Nd potentials used as Nd interaction. In both approaches, the binding energies, vertex constants, and asymptotic normalization coefficients in the N+d channel are calculated.     

A new model for calculating the binding energy of the lithium nucleus under the generalized Yukawa potential and Hellmann potential

In this paper, the Schrodinger equation for a 6-body system is studied. We solve this equation for the lithium nucleus by using a supersymmetry method with several specific potentials. These potentials are the Yukawa potential, the generalized Yukawa potential and the Hellmann potential. The results of our model for all calculations show that the ground state binding energy of the lithium nucleus with these potentials is very close to that obtained experimentally.     

Investigation of Hypernucleus Λ5He Structure and the Calculation of the Binding Energy

In this paper the nuclear structure of hypernucleus ₅^ΛHe and its effect on the binding energy B_Λ of A hyperon are systematically studied. The Polarization effect of the core a is explored. The binding energy B_Λ of ₅^ΛHe including D-state mixing component is calculated. The results show that the core α suffers a serious distortion by the interaction with Λ hyperon and has no longer the structure of a free Alpha Particle. The D-state mixing can improve the B_Λ calculated value about 0.5MeV. A Possible three cluster structure is further explored. The Λ+d+d model can give a B_Λ value close to the experimental one. The further exploration is necessary.     

Ground state of the 4α + Λ nucleus within the 4α+Λ cluster model

The s-wave bound state of the 4α+Λ system is investigated. The relevant solution to the Schrödinger equation is expanded in the basis formed by the eigenfunctions of Hamiltonian for the 4α subsystem. Differential equations for Yakubovsky components are employed to calculate basis functions. Phenomenological potentials for αα and αΛ interactions are used. In the 4α system, additional three-particle potentials for the interaction between α clusters are introduced in such a way as to reproduce the experimental data on the binding energies, the root-mean-square radii, and the charge form factors for the ¹²C and the ¹⁶O nucleus. The binding energy, the root-mean-square radius, and the hyperon distribution in the ground state of the _Λ ¹⁷ O nucleus are calculated. The results of the calculations are in good agreement with those obtained on the basis of the ¹⁶O+Λ two-particle model with the phenomenological Woods-Saxon potential.     

The real part of the nucleus-nucleus interaction

The real part of the interaction potential for several pairs of magic nuclei has been derived from the Skyrme interaction density functional. The matter density of each nucleus is described by a Fermi distribution adjusted to reproduce the Skyrme-Hartree-Fock densities. Exchange effects due to antisymmetrization are taken into account in an approximate way. The tail of the resulting potential can be accurately approximated with a Woods-Saxon shape beyond the inflexion point of the calculated potential. The parameters of these Woods-Saxon potentials show regularities with respect to the masses of the target and projectile. We have tested the validity of the real part of the potential against elastic scattering data by choosing an imaginary part with the same geometry and a variable strength. For the energy range we consider the calculated grazing angles are somewhat larger than the experimental ones.     

The volume contribution of the ion-ion optical potential from realistic complex nucleon-nucleon interaction

The real and imaginary parts of the optical model potential for several pairs of magic nuclei have been calculated by a double folding procedure. The complex effective interaction is calculated from the Reid soft core potential by solving the Bethe-Goldstone equation in two colliding nuclear matters. The calculated potentials were approximated with a Woods-Saxon shape. We studied the dependence of the parameters of these Woods-Saxon forms on the masses of the interacting nuclei.     

The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

The generalized pseudospectral (GPS) method is employed to calculate the bound states of the Hulthén and the Yukawa potentials in quantum mechanics, with special emphasis onhigher excited states andstronger couplings. Accurate energy eigenvalues, expectation values and radial probability densities are obtained through a non-uniform and optimal spatial discretization of the radial Schrödinger equation. Results accurate up to thirteen to fourteen significant figures are reported for all the 55 eigenstates of both these potentials withn <- 10 for arbitrary values of the screening parameters covering a wide range of interaction. Furthermore, excited states as high asn = 17 have been computed with good accuracy for both these potentials. Excellent agreement with the available literature data has been observed in all cases. Then > 6 states of the Yukawa potential has been considerably improved over all other existing results currently available, while the same for Hulthén potential are reported here for the first time. Excepting the 1s and 2s states of the Yukawa potential, the present method surpasses the accuracy of all other existing results in the stronger coupling region for all other states of both these systems. This offers a simple and efficient scheme for the accurate calculation of these and other screened Coulomb potentials.     

Alpha Cluster Structure of Hypernuclei and Λ-Seperate Energy of Λ17O

By using the alpha cluster structure model of hypernuclei and the phenomenological interaction potential between Λ hyperon and α-particle, the Λ seperate energy of the hypernucleus 13ΛC is calculated. A good agreement with the experimental data is achieved. Based on this the Λ-seperate energy of the hypernucleus 17ΛO is predicted. It is consistent with the empirical value of 17ΛO and advantages over the existing theoretical calculation made up-to-date.     

n-p pairing, Wigner energy, and shell gaps

The diagonal correlation energy due to n-n, p-p, and n-p pairing is shown to resolve the discrepancies between shell gaps determined from binding energy differences and the gaps calculated with Woods-Saxon potentials or with other mean-field models. The difference in diagonal correlation energy between an N=Z nucleus with filled shells and the nucleus with one less nucleon resolves this problem in lowest order. A previously derived result, that the diagonal correlation energy in the last occupied orbital for the latter nuclei is 1/2 of the equivalent correlation energy for closed shell nuclei, is tested against observed binding energies and found to be fairly accurate.     

Λ和∑粒子衰变的上下不对称性

本文计算结果指出,当强作用的影响被考虑以后,超子衰变的上下不对称的实验结果是可以解释的。对衰变的分析可以给出关于强作用的重正化和强度的重要知识。我们的结果指出强作用满足“强作用近似”的条件。     

Self-consistent calculations of hypernuclear properties with the Skyrme interaction

An extension of the Skyrme-Hartree-Fock formalism is proposed for calculating Λ binding energies (B_Λ) in hypernuclei throughout the periodic table. The calculation includes the self-consistent nuclear polarization by the Λ hyperon. Realistic estimates for ground state B_Λ's are obtained with a simple effective ΛN force and are compared with a Λ-nucleus potential model. The Λ particle excitation spectra have also been calculated. They are discussed in the context of strangeness analog state formation and the emphasis is put on the symmetry between Λ and nuclear states.     

Comparative Effect of an Addition of a Surface Term to Woods-Saxon Potential on Thermodynamics of a Nucleon

In this study, we reveal the difference between Woods-Saxon(WS) and Generalized Symmetric WoodsSaxon(GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schr¨odinger equation for the two potentials. The additional term squeezes the WS potential well, which leads an upward shift in the spectrum, resulting in a more realistic picture. The resulting GSWS potential does not merely accommodate extra quasi bound states, but also has modified bound state spectrum. As an application, we apply the formalism to a real problem,an α particle confined in Bohrium-270 nucleus. The thermodynamic functions Helmholtz energy, entropy, internal energy,specific heat of the system are calculated and compared for both wells. The internal energy and the specific heat capacity increase as a result of upward shift in the spectrum. The shift of the Helmholtz free energy is a direct consequence of the shift of the spectrum. The entropy decreases because of a decrement in the number of available states.     

Shell-model calculations with Woods-Saxon wave functions in O and Ca

Two-particle states of ¹⁸O and ⁴²Ca are calculated within the shell model. The nuclear cores are represented by Woods-Saxon potentials, and for the residual interaction, central forces of Yukawa and Gaussian types are used. The wave functions for the low-lying states except for the O₂⁺ and 2₂⁺ states in ⁴²Ca are obtained, and the calculated energy spectra are in good agreement with experiments. Also E2 transitions are calculated and compared with experimental results.     

Removal of singularities in the Coulomb and Yukawa potentials

A complex length is introduced into the Coulomb and Yukawa potential energy equations. It is shown how this complex length can be used to remove the small-distance singularities in the above potentials. In addition, the Yukawa potential now exhibits a hard core.     

Dynamical Structure of A≤4 Λ Hypernuclei

Based on variational method,we systematically studied the dynamical structures of A≤4 S shell Λ hypernuclei with the aid of the harmonic oscillator product expansions and the generalized Talmi-Moshinsiky transformation.We also made investigations on structures of the osdinary nuclei for A=2 and 3. By comparis on,we can see that the root mean distances between nucleons are shorten due to the presence Λ hyperon which compresses the core. Λ hyperon acts as the adhesive. The studies on internal structures of nuclear system show that the relative motions between particles are mainly in 0s orbits.     

Studying the general properties of potentials by means of dimensionless scaling variables

The general properties of the three-parametric Woods-Saxon potential and the two-parametric Hulthen and square-well potentials are studied by converting them to dimensionless scaling variables. The relations between the parameters of the potentials and such characteristics of a system as binding energies and the asymptotic normalization coefficients of wave functions are investigated.