A consistent set of nuclear rms charge radii: properties of the radius surface R(N,Z)

Angeli, I.

doi:10.1016/j.adt.2004.04.002

Cited by 682 publications

(329 citation statements)

References 44 publications

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“…The rms radius of the 28 Si density obtained from the analysis of the fusion data is shown in Table III. It is seen to be in very good agreement with the rms radius of the point-proton distribution that has been extracted from the measured rms charge radius [21].…”

Section: Densitiessupporting

confidence: 72%

Fusion ofSi28+Si28,30: Different trends at

et al. 2014

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Background:The fusion excitation function of the system 28 Si + 28 Si at energies near and below the Coulomb barrier is known only down to ≃15 mb. This precludes any information on both coupling effects on sub-barrier cross sections and the possible appearance of hindrance. For 28 Si + 30 Si even if the fusion cross section was measured down to ≃50µb, the evidence of hindrance is marginal. Both systems have positive fusion Q-values. While 28 Si has a deformed oblate shape, 30 Si is spherical.Purpose: Investigating: 1) the possible influence of the different structure of the two Si isotopes on the fusion excitation functions in the deep sub-barrier region; 2) whether hindrance exists in the Si+Si systems and whether it is strong enough to generate an S factor maximum, thus allowing a comparison with lighter heavy-ion systems of astrophysical interest.Methods: 28 Si beams from the XTU Tandem accelerator of INFN-Laboratori Nazionali di Legnaro were used. The set-up was based on an electrostatic beam separator, and fusion evaporation residues (ER) were detected at very forward angles. Angular distributions of ER were measured.Results: Fusion cross sections of 28 Si + 28 Si have been obtained down to ≃600 nb. The slope of the excitation function has a clear irregularity below the barrier but no indication of a S-factor maximum is found. For 28 Si + 30 Si the previous data have been confirmed and two smaller cross sections have been measured down to ≃4µb. The trend of the S-factor reinforces the previous weak evidence of hindrance. Conclusions:The sub-barrier cross sections for 28 Si + 28 Si are overestimated by coupled-channels calculations based on a standard Woods-Saxon potential, except for the lowest energies. Calculations using the M3Y+repulsion potential are adjusted to fit the 28 Si + 28 Si and the existing 30 Si + 30 Si data. An additional weak imaginary potential (probably simulating the effect of the oblate 28 Si deformation) is required to fit the low-energy trend of 28 Si + 28 Si. The parameters of these calculations are applied to predict the ion-ion potential for 28 Si + 30 Si. Its cross sections are well reproduced by including also one-and successive two-neutron transfer channels, besides the low-lying surface excitations.

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Section: Densitiessupporting

confidence: 72%

Fusion ofSi28+Si28,30: Different trends at

et al. 2014

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“…Notwithstanding the preceding, when comparing with the experimental binding energies [22] of 661.6 MeV for 76 Ge and 662.07 MeV for 76 Se we get a 0.5% underestimation in the calculation with the usual Sk3 force and a 2% overestimation in the calculation with the Sk3 ν force. Concerning the charge radii, the HF(Sk3) + BCS results are 4.12 fm for 76 Ge and 4.17 fm for 76 Se, whereas with increased spin-orbit strength one gets 4.09 fm for 76 Ge and 4.14 fm for 76 Se, which actually agree better with the experimental values of 4.08 fm for 76 Ge and of 4.14 fm for 76 Se [11].…”

supporting

confidence: 80%

“…The β values extracted from data in Refs. [10,11] are β = 0.13 for 74 Ge and β = 0.12 for 78 Se. The inclusion of experimental deformation and a larger spin-orbit strength for neutrons change also in this case the theoretical results toward a better agreement with the experimental data.…”

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confidence: 99%

“…The most precise data on the quadrupole moments of these nuclei come from Coulomb excitation reorientation measurements [10], which, together with experimental charge radii [11], give a deformation parameter β = 0.10 for 76 Ge and β = 0.16 for 76 Se (with 25%-30% uncertainty). These experimental deformations are taken into account when obtaining our theoretical occupation probabilities in the active shell and naturally lead us to check if the quadrupole deformation is responsible (fully or in part) for the disagreement between previous theoretical occupations and the experimental ones.…”

mentioning

confidence: 99%

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Theoretical mean-field and experimental occupation probabilities in the double-βdecay systemGe76to
Moreno
¹
,
Guerra
²
,
Sarriguren
³

et al. 2010
Phys. Rev. C
14
1
6
0
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Usual Woods-Saxon single-particle levels with BCS pairing are not able to reproduce the experimental occupation probabilities of the proton and neutron levels 1p 3/2 , 1p 1/2 , 0f 5/2 , and 0g 9/2 in the double-β decay system 76 Ge to 76 Se. Shifting down the 0g 9/2 level by hand can explain the data, but it is not satisfactory. Here it is shown that a self-consistent Hartree-Fock + BCS approach with experimental deformations for 76 Among double-β decay-with-two-neutrino processes, the best-studied case is that of 76 Ge going to 76 Se. Within a spherically symmetric description of these nuclei, the relevant proton and neutron single-particle levels involved in the double-β decay process are in the valence shells 1p 3/2 , 1p 1/2 , 0f 5/2 , and 0g 9/2 . Their occupation probabilities were measured recently by Schiffer et al.[1] (for neutrons) and by Kay et al. [2] (for protons). These data are not reproduced by previous mean-field calculations using Woods-Saxon potential and pairing within BCS approximation. By increasing the binding energy of the 0g 9/2 level, the agreement is better, because its occupation probability increases and eventually reaches the experimental one. This energy shifting has been performed by hand in previous works [3][4][5] to obtain the experimental occupation probabilities, and the resulting ground-state structure has been used to compute neutrinoless double-β matrix elements. Shell-model calculations [6] have also been carried out with occupation probabilities in good agreement with experimental ones, but the single-particle energies used are not available in the literature.In this work we use a deformed Skyrme Hartree-Fock (HF) mean-field with pairing correlations within BCS approximation. At each HF iteration the BCS equations are solved to get new single-particle wave functions i , energies e i , and occupation probabilities v 2 i until convergence is achieved. After convergence, the proton-neutron quasiparticle randomphase approximation (pnQRPA) equations are solved on each deformed ground-state basis for 76 Ge and 76 Se to get their Gamow-Teller (GT) strength distributions and to compute the two-neutrino double-β decay matrix element. The formalism is similar to that used in previous works [7][8][9] with an important difference. In this work we allow the Skyrme force parameters to vary and search for a parametrization that provides better agreement with the experimental occupations of the previously mentioned valence shells in 76 Ge and 76 Se, as well as in their neighbors. We focus on the effect of the spin-orbit strength, W 0 , which we find to be of primary importance for the desired description of proton and neutron valence-shell occupations.Experimental data and HF + BCS calculations suggest prolate deformations for the 76 Ge and 76 Se ground states. The most precise data on the quadrupole moments of these nuclei come from Coulomb excitation reorientation measurements [10], which, together with experimental charge radii [11], give a deformation parameter β = 0.10 for 76 Ge ...

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“…This positive value is in line with the result δ r 2 35,37 = +0.127 fm 2 that can be calculated from the rms of Angeli's compilation [42] that have been determined by averaging the charge radii extracted from different sources [43]. In view of the large dispersion of the nuclear data, we think that it is preferable to use the same reference for both isotopes to maintain some coherence.…”

Section: Isotope Field Shiftsupporting

confidence: 61%

Isotope shift on the chlorine electron affinity revisited by an MCHF/CI approach

Carette

Godefroid

2013

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. Today, the electron affinity is experimentally well known for most of the elements and is a useful guideline for developing ab initio computational methods. However, the measurements of isotope shifts on the electron affinity are limited by both resolution and sensitivity. In this context, theory eventually contributes to the knowledge and understanding of atomic structures, even though correlation plays a dominant role in negative ions properties and, particularly, in the calculation of the specific mass shift contribution. The present study solves the longstanding discrepancy between calculated and measured specific mass shifts on the electron affinity of chlorine [Phys. Rev. A 51, 231 (1995)].

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A consistent set of nuclear rms charge radii: properties of the radius surface R(N,Z)

Cited by 682 publications

References 44 publications

Fusion ofSi28+Si28,30: Different trends at

Fusion ofSi28+Si28,30: Different trends at

Theoretical mean-field and experimental occupation probabilities in the double-βdecay systemGe76to
Moreno
¹
,
Guerra
²
,
Sarriguren
³

et al. 2010
Phys. Rev. C
14
1
6
0
View full text Add to dashboard Cite

Isotope shift on the chlorine electron affinity revisited by an MCHF/CI approach

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A consistent set of nuclear rms charge radii: properties of the radius surface R(N,Z)

Cited by 682 publications

References 44 publications

Fusion ofSi28+Si28,30: Different trends at

Fusion ofSi28+Si28,30: Different trends at

Theoretical mean-field and experimental occupation probabilities in the double-βdecay systemGe76toMoreno1, Guerra2, Sarriguren3 et al. 2010Phys. Rev. C14160View full textAdd to dashboardCite

Isotope shift on the chlorine electron affinity revisited by an MCHF/CI approach

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About

Theoretical mean-field and experimental occupation probabilities in the double-βdecay systemGe76to
Moreno
¹
,
Guerra
²
,
Sarriguren
³

et al. 2010
Phys. Rev. C
14
1
6
0
View full text Add to dashboard Cite