scholarly journals The nth-order moment of the nuclear charge density and contribution from the neutrons

2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
Haruki Kurasawa ◽  
Toshio Suzuki

Abstract The relativistic expression for the $n$th-order moment of the nuclear charge density is presented. For the mean square radius (msr) of the nuclear charge density, the non-relativistic expression, which is equivalent to the relativistic one, is also derived consistently up to $1/M^2$ with use of the Foldy–Wouthuysen transformation. The difference between the relativistic and non-relativistic expressions for the msr of the point proton density is also discussed. The $n(\ge 4)$th-order moment of the nuclear charge density depends on the point neutron density. The fourth-order moment yields useful information on the msr of the point neutron density, and is expected to play an important role in electron scattering off neutron-rich nuclei.

2020 ◽  
Vol 18 (44) ◽  
pp. 33-39
Author(s):  
Sinaa Fahad Kadem ◽  
Altaf A. Al-Rahmani

The calculation. of the nuclear. charge. density. distributions. ρ(r) and root. mean. square. radius.( RMS ) by elastic. electron. scattering. of medium. mass. nuclei. such. as (90Zr, 92Mo) based. on the model. of the modified. shell. and the use of the probability. of occupation. on the surface. orbits. of level 2p, 2s eroding. shells. and 1g gaining. shells. The occupation probabilities of these states differ noticeably from the predictions of the SSM. We have found. an improvement. in the determination. of ground. charge. density. and this improvement. allow. more precise. identification. of (CDD) between. (92Mo- 90Zr) to illustrate the influence of the extra two protons on the charge. density. distributions and was agree. with those of experimental. data. and Hartree. – Fock. (H.F) wave. functions.


Author(s):  
Haruki Kurasawa ◽  
Toshimi Suda ◽  
Toshio Suzuki

Abstract The second-order moment of the nuclear charge density(R2c)is dominated by the mean square radius(msr) of the point proton distribution(Rp2), while the fourth-order moment(Q4c) depends on the msr of the point neutron one(R2n) also. Moreover, R2n is strongly correlated to R2c in nuclear models. According to these facts, the linear relationship between various moments in the nuclear mean field models are investigated with use of the least squares method for 40Ca, 48Ca and 208Pb. From the intersection points of the obtained straight lines with those of the experimental values for R2c and Q4c determined through electron scattering, the values of Rp and Rn are estimated. Since relativistic and non-relativistic models provide different lines, the obtained values of Rn and the skin thickness(Rn-Rp) differ from each other in the two frameworks.


2019 ◽  
Vol 13 (28) ◽  
pp. 68-81
Author(s):  
A. R. Ridha

The ground state proton, neutron and matter densities andcorresponding root mean square radii of unstable proton-rich 17Neand 27P exotic nuclei are studied via the framework of the twofrequencyshell model. The single particle harmonic oscillator wavefunctions are used in this model with two different oscillator sizeparameters core b and halo , b the former for the core (inner) orbitswhereas the latter for the halo (outer) orbits. Shell model calculationsfor core nucleons and for outer (halo) nucleons in exotic nuclei areperformed individually via the computer code OXBASH. Halostructure of 17Ne and 27P nuclei is confirmed. It is found that thestructure of 17Ne and 27P nuclei have 25 / 2 (1d ) and 1/ 2 2s -dominantconfigurations, respectively. Elastic electron scattering form factorsof these exotic nuclei are also studied using the plane wave Bornapproximation. Effects of the long tail behavior of the proton densitydistribution on the proton form factors of 17Ne and 27P areanalyzed. It is found that the difference between the proton formfactor of 17Ne and that of stable 20Ne (or of 27P and that of stable31P) comes from the difference in the proton density distribution ofthe last two protons (or of the last proton) in the two nuclei. It isconcluded that elastic electron scattering will be an efficient tool (inthe near future) to examine proton-halo phenomena of proton-richnuclei.


1993 ◽  
Vol 15 (4) ◽  
pp. 1-6
Author(s):  
Di Paola Mario ◽  
Nguyen Dong Anh

Stochastic linearization method is one of the most useful tools for analysis of nonlinear systems under random excitation. The fundamental idea of the classical stochastic linearization consists in replacing the original nonlinear equation by a linear one in such a way that the difference between two equations is minimized in the mean square value. In this paper a new version of the stochastic linearization is proposed. It is shown that for two nonlinear systems considered the new version gives good results for both the weak and strong nonlinearities.


2018 ◽  
Vol 56 ◽  
pp. 130-135
Author(s):  
M. V. Tserenyuk ◽  
O. M. Tserenyuk

In addition to assessing the absolute performance of animals, the impact of certain technological approaches, breeding influence and other external organized factors on the consolidation of pigs groups on certain grounds should be evaluated. Breeding consolidation is a desirable breeding process that is realized through more motivated consolidation of intra-breeding structural units for maintaining a significant level of intergroup differentiation and variability. If the issue relates to the rearing young animals that are introduced into the herd, this is the most urgent issue that needs to be monitored. The purpose of the research is to determine the consociality of the main signs of reproductive ability of the gilts, which are checked at different rates of artificial insemination of sows of the main herd. The research was carried out at the Shubs`ke farm in the Bogoduhivsky District of Kharkiv Oblast at the pig farm for the pure breeding of the Welsh breed pigs (breeding reproductive status from 2014). In order to evaluate the optimal multiplicity (from single to triple), a gilts with a total of 30 heads was selected. The main indicators of reproductive ability of gilts (multiplicity, weight of nest at birth and excommunication and keeping piglets before weaning on day 28) were evaluated. Recalculation on the weight of the litter at weaning at the weight of the nest at extermination in 60 days was carried out in accordance with the current instruction on the boning of pigs. The results of researches were worked out according to traditional methods by the method of variation statistics. Consolidation of individual indicators of reproductive capacity of gilts was calculated to the total number of evaluated animals. In the previous stage of the research, it was found that the use of multiple insemination of gilts compared to single insemination is positively reflected at the level of their reproductive ability. A decrease in the percentage of non-productive inseminants in animal groups has been established. Triple insemination of gilts allows for 1.14 piglets to be obtained more compared to single insemination of the same pigs (p < 0.01). Also, for three times insemination of gilts, in comparison with single insemination, larger nest for weaning were obtained (by 14.24 kg, converted to 60th day p < 0.01). At the same time, the reduction in the keeping of piglets to weaning for increase frequency of insemination of gilts. According to the multiplicity of gilts, the most consolidated level of symptoms per group was obtained for single insemination. Increasing the multiplicity of insemination negatively affected the consolidation of the multiplicity of the piglets (as for determining the coefficients of phenotypic consolidation due to the mean square deviation, so, and for determining the coefficient of variability). The least consolidated in terms of multiplicity were uterus for double insemination. It should also be noted that there is little difference, in general, on the indicators of the theonotypical consolidation of the multiplicity of piglets between different groups of animals. So this difference between the most contrasting groups was 0.447 points for determining the coefficients due to the mean square deviation and 0.397 points for the determination due to the coefficient of variability, respectively. By weight of the same litters at birth, the most consolidated group was gilts, which was inseminated twice. The least consolidated are trimmed three times, respectively. The difference as a whole, according to the indicators of the theonotype consolidation of the mass of the litter’s piglets at birth, between different groups of pigs was even smaller. The difference between the most contrasting groups was 0.270 points for determining the coefficients due to the mean square deviation and 0.260 points for the determination due to the coefficient of variability, respectively. On the basis of the mass of the litter at weaning, the most consolidated level of symptoms was obtained in the group of gilts for triple insemination. The least consolidated group, respectively, was gilts for single insemination. At the same time, on the basis of the weight of the litter at weaning, the slightest differences were obtained after the consolidation of the signs between different groups of pigs. The difference between the most contrasting groups was 0.173 points for determining the coefficients due to the mean square deviation and 0.248 points for the determination due to the coefficient of variation, respectively. At different rates of insemination of gilts, there are no significant differences between the groups between the groups in terms of the consolidation of signs of reproductive ability. Also, there was no clear effect on increasing the multiplicity of insemination of gilts to the consolidation of their signs of reproductive qualities.


It is pointed out that optical isotope shifts between even-even isotopes in the medium-heavy elements show variations which are similar from one element to another, and that these variations are associated with particular values of N – Z , where N and Z refer to neutron and proton numbers respectively. Since the isotope shifts depend on differences in the mean square radii of the nuclear charge distribution, this correlation is evidence for some degree of a-particle structure in these nuclei. Further evidence from the energies of the first excited levels of the nuclei is also briefly considered.


1993 ◽  
Vol 71 (3-4) ◽  
pp. 162-164
Author(s):  
Cihat Ozhasoglu ◽  
M. L. Rustgi

A two-parameter Fermi-type charge-density distribution is used to determine the Coulomb energy of a nucleus of a given charge Z. The expression is used to determine the nuclear charge-density-radius parameter, r1, and the diffuseness parameter, a, from the maximum kinetic energies in the β+-decay experiments. The deduced parameters r1 and a are compatible with the values obtained from the analyses of electron-scattering experiments.


2009 ◽  
Vol 87 (7) ◽  
pp. 807-815 ◽  
Author(s):  
George A. Noble ◽  
William A. van Wijngaarden

Precise isotope shift and fine structure measurements are critically reviewed. Each experiment was checked for whether the data found for different transitions yielded consistent values for the difference in mean-square nuclear charge radius Δr2 of 6,7Li. Experiments that passed this test found Δr2 = 0.735 ± 0.036, 0.755 ± 0.023, and 0.739 ± 0.013 fm2 by studying the Li+ 1s2s 3S→1s2p 3P transition, the Li D lines and the Li 2S1/2→3S1/2 transition, respectively. These data determine the difference in mean-square nuclear charge radius 25 times more accurately than electron scattering. Similarly, averaging the fine structure data from the same experiments gives 62 678.75 ± 0.55 MHz for the 7Li+ 1s2p 3P1–2 interval, in good agreement with theory. The results for the 6,7Li 2P fine structure intervals, 10 0.52.954 ± 0.049 and 10 053.154 ± 0.040 MHz, exceed computed values by 2 MHz and yield a splitting isotope shift, which is nearly a factor of 2 lower than a theoretical estimate.


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