The charge-distribution differences of 209Bi, 208, 207, 206, 204Pb and 205, 203Tl investigated by elastic electron scattering and muonic X-ray data

Euteneuer, H.; Friedrich, J.; Voegler, N.

doi:10.1016/0375-9474(78)90143-4

Cited by 95 publications

(39 citation statements)

References 30 publications

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“…For comparison we have included the R. Bhattacharya: Single Particle Spin-Orbit Potential Table 3 we list the parameters of the present potentials for both the neutron and the proton states. It is apparent from Table 2 Table 4 we present the result of our analysis along with the experimental result [9]. The agreement obtained speaks for the method used.…”

Section: Pacs: 2110pcsupporting

confidence: 61%

On the geometrical shape of the single particle spin-orbit potential

Bhattacharya

1985

Z Physik A

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A good description of the single particle shell model states near the Fermi surface, after including core polarization correction, can be obtained by taking identical geometrical shapes for both central and spin orbit potential thus reducing the number of free parameters in the scattering analysis. This bary centric approach also reproduces the charge distribution admirably. PACS: 21.10.PcThe physical picture behind the nuclear structure studies through nuclear reactions is describable in terms of an average one-body potential. Though the replacement of the interactions among the nucleons by the average potential is a drastic simplification, yet it is a common practice. This one-body potential consists of mainly two parts -a central potential of realistic nature (Woods-Saxon type), and a spin-orbit potential necessary for description of spin dependent interactions. The simplest approach is to write down the forms that are allowed by general invariance arguments [1]. Greenlees and Pyle [2] established in a systematic and careful analysis of the proton elastic scattering cross-sections and polarization data over a wide mass region between 4~ and 2~ that the radius parameter rso of the spin orbit potential is smaller than that of the central part of the Woods-Saxon potential used. This difference of radial extent has been interpreted by Greenlees, Pyle and Tang [3] in terms of the short range character of the nucleon-nucleon spin-orbit interaction. This difference of geometry in central and spin-orbit potential was further high lighted in the work of Rost [4]. In the case of 2~where the single particle picture has maximum validity, Rost obtained better Z 2 for both neutron and proton states, by using different radius parameters for central and spin-orbit potential. Rost's suggestion of using r~o=0.75r o is now widely accepted in calculating the single particle energies and wave functions for a wide range of nuclei and has been found to be crucial for the evaluation of the shell gap in the super heavy region [5]. In a recent reevaluation [6] of parameters of the Woods-Saxon potential which generates the single particle spectrum near the Fermi surface of 2~ results were obtained in tune with the earlier findings. It has also been proven [7] that even in lower shell region one can generate the requisite level bunching effect by altering only the strengths of central and spin-orbit potentials. However, in the present work we will show that this difference in geometrical shape is not the only solution for obtaining a reliable spectrum of single particle states of closed shell nuclei. It has been conclusively shown that there is another way of getting a unique set of Woods-Saxon parameters, identical in geometry for both the central and spin-orbit components, which gives good Z2-fit with the observed single particle spectra of 2~ We first calculate the bary centers of the different spin-orbit doublets (SOD) for the proton and neutron states in 2~ from the observed single particle spectra [6]. The binding energies of the...

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Section: Pacs: 2110pcsupporting

confidence: 61%

On the geometrical shape of the single particle spin-orbit potential

Bhattacharya

1985

Z Physik A

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“…We obtained them by unfolding the charge densities determined from electron scattering [43] and muonic x rays (see also Ref. [44]).…”

Section: Methods Of Determination Of Thementioning

confidence: 99%

Extraction of neutron densities from elastic proton scattering byPb206,207,208
Starodubsky
¹
,
Hintz²
1994
Phys. Rev. C
146
10
164
0
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The method for extraction of neutron and matter densities from data on cross sections and spin observables for elastic p-nucleus scattering is presented. The effective nuclear potential was treated to the 6rst order with respect to the t-matrix and density distributions. To eliminate uncertainties associated with the t matrix, the latter has been determined directly from p-Ca scattering data, where the proton and neutron densities are known sufBciently well. The medium modi6cations in the t matrix have been included by means of density dependent terms added to the free t matrix.The neutron densities to be found were expressed as a Hartree-Fock (HF) distribution plus a small correction expanded in a Fourier-Bessel series with inclusion of only low-frequency components determined by the data. High-frequency components are presented by the HF term. Expressions for the physical observables were linearized in terms of the expansion coefficients, the latter being determined through an iterative procedure from the y criterium. The method enables one to obtain statistical Quctuations in those Fourier components as they are generated by experimental error bars. The normalization and model uncertainties have been also estimated. The extracted densities of ' ' Pb and their differences were compared with the HF results calculated by us with the Skyrme interaction. On the whole, pretty good agreement has been achieved.PACS number(s): 21.10. Gv, 25.40.Cm, 21.30. +y, 27.80.+w

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“…For 208 Pb, the charge distribution has been measured by electron scattering [34]. Figure 1 shows the calculated density distributions with comparison with the experimental charge density.…”

Section: A Density Distributions Of Spherical Nucleimentioning

confidence: 99%

Density distributions of superheavy nuclei

2005

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We employed the Skyrme-Hartree-Fock model to investigate the density distributions and their dependence on nuclear shapes and isospins in the superheavy mass region. Different Skyrme forces were used for the calculations with a special comparison to the experimental data in 208 Pb. The ground-state deformations, nuclear radii, neutron-skin thicknesses and α-decay energies were also calculated. Density distributions were discussed with the calculations of single-particle wave functions and shell fillings. Calculations show that deformations have considerable effects on the density distributions, with a detailed discussion on the 292 120 nucleus. Earlier predictions of remarkably low central density are not supported when deformation is allowed for.

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The charge-distribution differences of 209Bi, 208, 207, 206, 204Pb and 205, 203Tl investigated by elastic electron scattering and muonic X-ray data

Cited by 95 publications

References 30 publications

On the geometrical shape of the single particle spin-orbit potential

On the geometrical shape of the single particle spin-orbit potential

Extraction of neutron densities from elastic proton scattering byPb206,207,208
Starodubsky
¹
,
Hintz²
1994
Phys. Rev. C
146
10
164
0
View full text Add to dashboard Cite

Density distributions of superheavy nuclei

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The charge-distribution differences of 209Bi, 208, 207, 206, 204Pb and 205, 203Tl investigated by elastic electron scattering and muonic X-ray data

Cited by 95 publications

References 30 publications

On the geometrical shape of the single particle spin-orbit potential

On the geometrical shape of the single particle spin-orbit potential

Extraction of neutron densities from elastic proton scattering byPb206,207,208Starodubsky1, Hintz2 1994Phys. Rev. C146101640View full textAdd to dashboardCite

Density distributions of superheavy nuclei

Contact Info

Product

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About

Extraction of neutron densities from elastic proton scattering byPb206,207,208
Starodubsky
¹
,
Hintz²
1994
Phys. Rev. C
146
10
164
0
View full text Add to dashboard Cite