Electrostatic potentials for nucleus-nucleus optical model

Jain, Anupriya; Gupta, Monika; Shastry, C. S.

doi:10.1103/physrevc.12.801

Cited by 12 publications

(11 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More than 25 years ago [5][6][7][8][9] the role of more realistic descriptions of the Coulomb interaction between two heavy-ions was investigated.…”

mentioning

confidence: 99%

Analytical approximation for the sphere-sphere Coulomb potential

Anni

2001

Phys. Rev. C

View full text Add to dashboard Cite

A simple analytical expression, which closely approximates the Coulomb potential between two uniformly charged spheres, is presented. This expression can be used in the optical potential semiclassical analyses which require that the interaction be analytic on and near the real r-axis. PACS number(s): 24.10. Ht, 25.70.Bc, 03.65.Sq The semiclassical analyses of the optical potential cross sections play an important role in understanding the scattering mechanism of light-and heavy-ions [1]. The direct evaluation of the semiclassical amplitudes is based on the calculation of the integral actions between the turning points of the radial motion. The turning points of the radial motion are solution of the equationwhere k, λ, E, and U (r) are, respectively, the wave number, the angular momentum in units of , the center of mass energy, and the complex optical potential. The integral actions are defined bywhere r i and r j are appropriate solutions of Eq. (1). In the semiclassical approximations both these quantities are treated as analytical functions of λ around the real λ-axis. This is true only if the complex optical potential is an analytical function of r, on and near the real r-axis.In the phenomenological analyses the optical potential between heavy-ions is written in the formwhere V (r) and W (r) are the real and the imaginary part of the nuclear interaction, and V C (r) is the Coulomb interaction potential. As a rule, analytic functions are used for the real and the imaginary part of the interaction. On the contrary, the Coulomb part of the interaction is described using either the Coulomb potential of one point charged particle with a uniformly charged sphere of radius R C (in the least recent works) or the Coulomb potential between two uniformly charged spheres of radii, say, R 1 and R 2 (in the more recent ones). These potentials are not analytic functions around the real r-axis.This fact, rigorously, excludes the possibility of applying the semiclassical methods which assumes the analyticity of the potential. The lack of analyticity must however be considered accidental. It arises from our preference to use simple expressions for the interaction, and we do not really think that it is connected with some physical fact. Owing to this we expect that this, and similar troubles, can be cured with a little effort.To do this we here briefly recall some techniques used in the past to treat the point-sphere case, and we present a similar method for the sphere-sphere case.Both these Coulomb potentials can be written in the form

show abstract

“…More than 25 years ago [5][6][7][8][9] the role of more realistic descriptions of the Coulomb interaction between two heavy-ions was investigated.…”

mentioning

confidence: 99%

Analytical approximation for the sphere-sphere Coulomb potential

Anni

2001

Phys. Rev. C

View full text Add to dashboard Cite

show abstract

“…These considerations are in contradiction to the misconception in the conclusions of [5]. For a= 1 the SSC-potential lies 20 % lower than the PSC-potential (100%).…”

Section: Sphere-sphere Coulomb (Ssc) Potentialmentioning

confidence: 65%

“…In contrast to an often applied assumption it is seen that inside the nucleus two uniform charged spheres provide only a relatively poor approximation. At this point it should be appropriate to make some remarks concerning the work of Jain et al [5] referred to above. The authors show that the Coulomb potential between nuclei having arbitrary charge distributions can be expressed in terms of a triple integral.…”

Section: Comparison Of the Realistic And The Ssg-potentialmentioning

confidence: 99%

“…The comparison of the results with the SSC-potential has shown [3] that form and magnitude of the reduced Coulomb repulsion do not essentially differ for different charge distributions in the surface region. In the papers of Huizenga [4] and Jain et al [5] then Coulomb potentials have been compared deduced from various forms of the nuclear charge distribution of the target and projectile. A first attempt to solve the Coulomb potential problem analytically has been published by Jain et al [5].…”

Section: Introductionmentioning

confidence: 99%

“…In the papers of Huizenga [4] and Jain et al [5] then Coulomb potentials have been compared deduced from various forms of the nuclear charge distribution of the target and projectile. A first attempt to solve the Coulomb potential problem analytically has been published by Jain et al [5]. They succeded in reducing the integral for the Coulomb potential using special charge distributions for the collision partners, to an algebraic expression which, however, without mentioning its rather complicated structure contains a single integral yet.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Coulomb potentials between spherical heavy ions

Iwe

1982

Z Physik A

View full text Add to dashboard Cite

The Coulomb interaction between spherical nuclei having arbitrary radial nuclear charge distributions is calculated. All these realistic Coulomb potentials are given in terms of analytical expressions and are available for immediate application. So in no case a numerical computation of the Coulomb integral is required. The parameters of the charge distributions are taken from electron scattering analysis. The Coulomb selfenergies of the charge distributions used are also calculated analytically in a closed form. For a number of nucleus-nucleus pairs, the Coulomb potentials derived from realistic charge distributions are compared with those normally used in various nucleusnucleus optical model calculations. In this connection a detailed discussion of the problem how to choose consistently Coulomb parameters for different approximations is given.

show abstract