Shell Closure Effects Research Articles

Global optical-model analysis of the elastic deuteron scattering from medium heavy target nuclei

Angular distributions for the cross section and the analyzing powers iT 11, T 20, T 21 and T 22 in the angular range 20°–175° (lab) have been measured for 12 MeV deuterons scattered elastically from several medium-heavy, spin-zero target nuclei. The data have been analysed using an optical model including complex spin-orbit and tensor terms. With a few exceptions, excellent fits have been obtained to all the measured quantities, yielding a set of global parameters. The depths of the central part of the optical potentials are correlated and depend on the structure of the target nuclei. Contrary to the results for selenium, which exhibit clear shell-closure effects that are well reproduced by optical-model calculations, the data for N = 28 nuclei were found to be very difficult to describe. Irregularities in the optical-model parameters and problems in fitting the measurements are discussed. Possible ways of improving the theoretical description of deuteron scattering are suggested.

Independent yields of fast-neutron fission ofTh232: Observation of proton odd-even effect and neutron shell effect on the yields

Elemental yields in the fission of $^{232}\mathrm{Th}$ induced by reactor neutrons were measured and found to disclose a pronounced odd-even effect. Independent and cumulative yields of isotopes of Kr, Xe, Sn, and Sb were measured and the independent yields of isotopes of Rb, Cs, and Sb were subsequently derived. A comparison of the yield values obtained with the calculated "normal" yields reveals a constant enhancement of products with an even number of protons, relative to those with an odd number. An average amplitude of 30(\ifmmode\pm\else\textpm\fi{}12)% in the fluctuation of proton pairing was established for all isotopes measured, except for the doubly magic $^{132}\mathrm{Sn}$, which shows an extreme effect, apparently due to its closed neutron shell. The odd-even effect is discussed in connection with the mass distribution, excitation, and total kinetic energies. The neutron shell effect on the yields is discussed with regard to the primary mass split and the neutron emission probabilities.[NUCLEAR REACTIONS, FISSION Fission yields $^{232}\mathrm{Th}(n,f)$, calculated proton odd-even effect, calculated neutron closed shell effect.]

Shell closure effects in the elastic scattering of polarized deuterons

An enhancement of the analysing powers i T 11 ( θ) and T 20 ( θ) with increasing nuclear mass of the target nuclei is reported for 76,78,80,82 Se( d, d) elastic scattering at 12 MeV. Shell closure effects are proposed to account for this effect.

Alpha-preformation in even-even alpha emitters: An alpha-decay without tunnelling approach

An ‘alpha-decay without tunnelling’ approach shows that alpha-preformation probability in trans-lead even-even alpha-emitters lies in the range of 0·17–0·08, indicating a clear shell-closure effect atN = 126 and exhibits appreciably enhanced values in open-shell nuclei and executes a zig-zag nature with increasing neutron number in an isotopic series. All these findings are in fair qualitative agreement with experimental observations. Experimental results are found to overestimate this parameter for these heavy deformed nuclei.

The closed-shell effect on fission barriers at Z = 82 and N = 126

A method is suggested for the separation of the overlapping proton and neutron closed-shell effects on experimental fission barriers at Z = 82 and N = 126.

Systematics of nuclear charge distributions in Fe, Co, Ni, Cu, and Zn deduced from muonic x-ray measurements

The results of precise measurements of the energies of the $2{p}_{\frac{3}{2}}\ensuremath{\rightarrow}1{s}_{\frac{1}{2}}$ and $2{p}_{\frac{1}{2}}\ensuremath{\rightarrow}1{s}_{\frac{1}{2}}$ muonic x-ray transitions of $^{54}\mathrm{Fe}$, $^{56}\mathrm{Fe}$, $^{57}\mathrm{Fe}$, $^{58}\mathrm{Fe}$, $^{59}\mathrm{Co}$, $^{58}\mathrm{Ni}$, $^{60}\mathrm{Ni}$, $^{61}\mathrm{Ni}$, $^{62}\mathrm{Ni}$, $^{64}\mathrm{Ni}$, $^{63}\mathrm{Cu}$, $^{65}\mathrm{Cu}$, $^{64}\mathrm{Zn}$, $^{66}\mathrm{Zn}$, $^{68}\mathrm{Zn}$, and $^{70}\mathrm{Zn}$, are reported. Using a highly linear digitally stabilized Ge(Li) spectrometer system, the absolute energies and energy shifts between nuclei were measured with total errors of approximately 40-60 eV (110 eV for $^{70}\mathrm{Zn}$). The data were analyzed in terms of the Barrett moments $〈{r}^{k}{e}^{\ensuremath{-}ar}〉$ of the nuclear charge distributions from which the equivalent nuclear radii ${R}_{k}$ and the isotopic and isotonic differences $\ensuremath{\delta}{R}_{k}$ were computed. Particular attention was given to higher-order corrections of the energies of the muonic states. Appropriate quantum-electrodynamical corrections were calculated to all significant orders. Nuclear polarization corrections for multipole interactions up to and including $L=4$ were computed for each isotope. The $\ensuremath{\Delta}A=2$ isotone shifts $\ensuremath{\delta}{R}_{k}$ for even $A$ isotopes show a strong shell closure effect at $Z=28$, which is quite independent of the neutron number. The $\ensuremath{\Delta}N=2$ isotope shifts between even nuclei decrease smoothly and uniformly with increasing $N$ from $N=28$ to $N=40$ and are essentially independent of $Z$. This unexpected behavior suggests that the added neutrons interact with the entire proton core rather than with the valence protons. The $\ensuremath{\Delta}N=1$ isotope shift results show a pronounced odd-even staggering effect, which, however, is somewhat smaller than theoretical predictions. The isotone series $^{58}\mathrm{Fe}$-$^{59}\mathrm{Co}$- $^{60}\mathrm{Ni}$, which is just below the $Z=28$ shell closure, shows strong odd-even staggering, whereas the series $^{64}\mathrm{Ni}$- $^{65}\mathrm{Cu}$-$^{66}\mathrm{Zn}$ and $^{62}\mathrm{Ni}$-$^{63}\mathrm{Cu}$- $^{64}\mathrm{Zn}$ just above $Z=28$ exhibit only a very small staggering effect. A comparison of the experimental data of the rms radii ${〈{r}^{2}〉}^{\frac{1}{2}}$ with the results of spherically constrained Hartree-Fock calculations shows good agreement for all four Zn isotopes and the heavier Ni isotopes ($^{60}\mathrm{Ni}$, $^{62}\mathrm{Ni}$, $^{64}\mathrm{Ni}$), but poor agreement for the Fe isotopes and $^{58}\mathrm{Ni}$.NUCLEAR STRUCTURE, MOMENTS $^{54,56,57,58}\mathrm{Fe}$, $^{59}\mathrm{Co}$, $^{58,60,61,62,64}\mathrm{Ni}$ $^{63,65}\mathrm{Cu}$, $^{64,66,68,70}\mathrm{Zn}$; measured muonic x-ray spectra; deduced nuclear charge parameters, isotope and isotone shifts. Calculated quantum-electrodynamic and nuclear-polarization corrections. Compared charge parameters with Hartree-Fock calculations.

Establishment of Neutron Shell Effects in (n, 2n) Cross-Sections at 14 MeV

The existence of shell effects in ( n , 2 n ) cross-sections at 14 MeV neutron energy has been controversial for more than a decade. In the present work, recently available systematised data on ( n , 2 n ) cross-sections at 14.7 MeV has been reinvestigated critically in the vicinity of closed shells. These plots of σ( n , 2 n ) versus N and ( N - Z )/ A show definite shell effects at N =20,28 and 50 which have never been revealed so distinctly by earlier investigations. The disappearance of shell effect in heavy nuclei N =82 has been explained. It has been demonstrated that shell closure effect is perceptible clearly only in comparison to neighbouring nuclei of same N - Z and pairing effects. The distinct sharp rise of σ ( n , 2 n ) with ( N - Z )/ A >∼0.1, has been noted to be a characteristic of closed shell or sub-shell isotones only. An empirical relation for σ( n , 2 n ) is devised, for A ≧110.

Damping of nuclear dipole states

The connection between the photoabsorption cross section and the response of a system to a weak external electromagnetic field is exploited to study the absorption of γ-rays by nuclear systems. In the nuclear shell model, the response function is expressed in terms of the particle-hole excitations that are induced by the external field. The effect of collisions between excited particle-hole pairs and the nuclear background leads to a damping of such particle-hole excitations. We show that this damping can be reexpressed in terms of the individual damping widths of particles and holes in an interacting system. However, these damping widths have to be evaluated off the energy shell due to the requirement of energy conservation between eigenmodes of the ordinary shell model and the more complicated states that are responsible for their damping. The net effect of collisions is thus to replace the undamped particle-hole excitations of the shell model by damped quasiparticle-quasihole excitations, whose widths depend, however, on the excitation energy of the system. We construct new dipole states out of such excitations and show that the associated absorption cross section for γ-rays contains resonances at energies corresponding essentially to the dipole energies given by the ordinary shell model. However, the quasiparticle nature of the excitations introduces a new feature into the problem in that the new dipole states have a finite width. This width is determined by the average off-shell width of the quasiparticle-quasihole pairs at the excitation energy of each dipole state. The profile of the associated photoabsorption cross section is given by a sum of Breit-Wigner line shapes in a Tamm-Dancoff (TDA) calculation of the dipole excitations. If ground-state correlations are included via a random-phase-approximation (RPA) calculation, the profile of the resulting photoabsorption curve is approximately given by a sum of Lorentz, instead of Breit-Wigner line shapes. The dipole sum rules turn out to be the same in the ordinary shell model and its extension that includes quasiparticle damping. Since one does not have direct experimental access to the off-shell damping widths of individual particles and holes that are required in this description of dipole excitations, we have attempted to infer this information from known optical model potentials for nucleon-nucleus scattering. Combining such a procedure with a schematic particlehole model to simulate the shell-model ingredients required by our approach, we have calculated the photoabsorption in 208Pb. The model reproduces the main features of the experimental curve and we obtain a width ranging from 2 to 5 MeV ( Γ exp ⋍ 4 MeV ) depending on which optical potential is used. In this connection it is essential to use optical potentials that are specific to 208Pb and thus take into account the effect of shell closure on the absorptive part of the optical potential. The effect of an energy-dependent damping on the absorption curve is also illustrated in the schematic model. For instance a variation like ( ϵ − μ) 2 in the quasiparticle widths (μ is the chemical potential), allows particle-hole excitations at lower energies to appear as fine-structure resonances while at the same time giving the correct width to the giant dipole state. Fine structure of a similar nature is found experimentally in 208Pb.

S-and P-wave neutron spectroscopy, part Xa: Intermediate structure, 2 p−1 h states

Feshbach, Kerman, and Lemmer's doorway-state theory of intermediate structure is applied to the investigation of neutron doorway escape widths, Γ d ↑ . Assuming that the target nuclei in the ground states are spherical in nature, the three compound nuclei 91Zr, 89Sr, and 49Ca are considered as test cases. A basis of 2 p−1 h states in each of the above three compound nuclei is diagonalized via an effective two-body interaction. Doorway states of various angular mementa and of both parities are considered for the nuclei under investigation. Throughout the entire calculation proper Woods-Saxon potentials are used to generate both the neutron and proton wavefunctions. In the case of 89Sr, and 91Zr, the calculated p-wave escape widths are large compared to the s-wave widths in the low energy region. This is a manifestation of the single particle giant resonance phenomenon. The effect of shell closure is evident in 49Ca in that the predicted spacing of levels is large; for instance, the lowest predicted s-wave doorway is about 1.5 MeV. For comparison with low energy (En ⩽ 1.4 MeV) neutron scattering data, the sum rule Σγ n 2 = γ d 2 is employed, and the effect of doorway states on the local strength function and the fine structure observed is discussed. In general, it can be said that the calculations are consistent with all the available experimental data which are not extensive enough to verify all the details of the calculations. For instance, it is only possible to conclude that the 2 p−1 h structure is an alternative representation of these doorway states, the other possibility being the excited core picture which seems to be confirmed for Pb.

Independent yields of 133I, 134I, and 135I in the thermal neutron induced fission of 233U and 239Pu: Effect of the 82-neutron shell closure on charge distribution

By the rapid chemical isolation of iodine via exchange on a performed AgCl precipitate, the fractional independent yields of 133I, 134I, and 135I in the thermal neutron induced fission of 233U and 239Pu have been measured to be 0·137 ± 0·013, 0·331 ± 0·020, and 0·606 ± 0·024, respectively, for 233U fission, and 0·151 ± 0·028, 0·335 ± 0·025, and 0·608 ± 0·017, respectively, for 239Pu fission. The deviations quoted are standard deviations. The results are discussed in terms of the effect of the closed 82-neutron shell on charge distribution in fission: both scission of the compound nucleus into fragments and subsequent evaporation of neutrons appear to be influenced by the closed 82-neutron shell.

Division of nuclear charge in the thermal neutron fission of U235

The mean primary nuclear charges of fragments from thermal neutron fission of U235 as a function of initial mass in the range 88–105 have been determined from theK-ray energy spectra of the light fragments.K- rays were registered with an argon-methane filled proportional counter in coincidence with the pulses from a pair of semiconductor detectors for complementary fission fragments. The deviation of the mean primary charge of the fragments from the “unchanged charge density” value as compared to the density of the parent nucleus U236 was found to be 0.54±0.14 charge units independent of mass in the range 88–105. No closed shell effect on the mean primary charge was found.

Neutron shell effects in the (n, 2n) cross-sections at 14 MeV

The systematics of the available total (n, 2n) reaction cross-sections for 14 MeV neutrons have been investigated for even-neutron target nuclei. The existence of neutron shell effects is found and discussed on the background of the statistical theory. Minima in the (n, 2n) cross-sections at the magic neutron numbers N=28 and 50 for even and N=20 for odd-proton target nuclei can be accounted for by similar trends in the Q values. Cross-section maxima at the closed neutron shells N=82 and 126 for even and N = 28, 50, 82 and 126 for odd-proton target nuclei can be understood as an effect of shell closure on the nuclear level density, the relative decrease of which on passing across a closed shell is larger for higher excitation energies. The (n, n′γ) reaction is the principal one competing with the (n, 2n) process at 14 MeV in the medium and heavy mass regions. Since for the (n, n′γ) reaction the residual excitation energies lies in the region up to 12 MeV, whereas for the (n, 2n) reaction, it does not exceed 4 MeV, and since the relative change in the level density is greater at the higher excitation energies, the competition between (n, n′γ) and (n, 2n) reactions favours the latter in the region of closed neutron shells and thus accounts for the observed maxima in the (n, 2n) cross-section systematics.

Study of shell closure effect on proton total reaction cross sections

Study of shell closure effect on proton total reaction cross sections

The effect of shell closure on the angular distribution of elastically scattered particles

In elastic scattering from nuclei, the vector analyzing powers of polarized deuterons are found to be strongly affected by the imaginary parts of optical potentials. A definite relationship is postulated between the analyzing power and the imaginary potential depth. The relationship shows that the shell-closure effect of the analyzing power observed for Se isotope targets is the reflection of the isotope dependence of the imaginary potential. Coupled-channel calculations show that some low-lying levels of the target nuclei are responsible for the isotope dependence. By the use of the relationship, deuteron scattering from medium-weight nuclei at incident energies of about 15 MeV are reanalyzed to give a systematic variation with target mass number for the potential parameters, which is emphasized by a nearly constant volume integral of the real potential per pair of interacting nucleons.

Isotopic, Isotonic, and Shell Closure Effects on the Large-Angle Scattering of Polarized Protons

Detailed measurements on the elastic scattering of 14Mev polarized protons out to 170 nif- in the laboratory reference frame are reported. The nuclides studied are in the mass region 50-70 and encompass closed shells of neutrons and protons. The measurements comprise left-right asymmetries that are related to the polarization that would result from the elastic scattering of an unpolarized proton beam. Results obtained on a series of isotopes and isotones from Cr to 2n are given. (C.E.S.)

Asymmetric Fission of Bismuth

An asymmetric mode of mass division in the mass region 66-73 has been observed in the fission of ${\mathrm{Bi}}^{209}$ with 36-Mev protons. About 0.3% of the fissions contribute to this mode. At 58 Mev no evidence for asymmetric fission (0.05% of total fissions) as a separate mode could be found. The fission cross sections at 36 and 58 Mev are 1.9 and 11.3 mb, respectively. The narrowness of the 36-Mev asymmetric peak leads to the suggestion that the asymmetric fission of bismuth results from the fission of a single nuclear species and from a closed-shell effect, similar to the fine structure observed in low-energy fission of heavy elements. This asymmetric fission is considered to occur from states of relatively high excitation energy. However, the possibility of asymmetric fission also occurring from states of low excitation energy, whether following neutron evaporation or as a consequence of an inelastic proton interaction, cannot be ruled out. The symmetric fission observed with both 36- and 58-Mev protons is consistent with the results obtained by Fairhall in the fission of bismuth with 22-Mev deuterons.

Intrinsic quadrupole moments of deformed nuclei and superfluidity in nuclei

Intrinsic quadrupole moments of deformed nuclei are calculated on a completely particle picture as a function of the atomic number Z and the parameter of spheroidal distortion of the well in which the independent particles move. The effects of the pairing force responsible for the superfluid property of the existence of an energy gap are examined by using the Green's function method of Migdal. The deformation of the single-particle potential well is treated (a) as a perturbation and (b) exactly, by using the Nilsson and Mottelson-Nilsson energy spectra and wave functions. It is necessary to include the configuration mixing with the major harmonic-oscillator shells N' = N±2 caused by the deformation. In order to account for the observed quadrupole moments, slightly smaller values of the Nilsson deformation parameter are required than those following from the uniform-charge model. The effect of the energy gap is to smear out the shell-closure effects. As a result, the dependence of quadrupole moments on Z is similar to that predicted by the uniform-charge model.

Nuclear Deformation and the Photodisintegration Giant Resonances

The effects of nuclear deformation and shell closure upon the photodisintegration giant resonances have been investigated by measuring the (γ,n) cross sections for seven isotopes with 82 ≤ N ≤ 108 using the bremsstrahlung from the 33 MeV Canberra electron synchrotron. The induced radioactivities were measured with a NaI (T1) scintillation spectrometer. The most accurate results were obtained for the 181Ta (γ,n) reaction leading to the 8.15 hour isomeric level of 180Ta, the yield of which was measured to ½% statistical accuracy at 250 kev intervals over the rising part of the activation curve. The giant resonance for the reaction measured in this way has a width of 5.3 MeV and shows no evidence for the splitting into two components predicted by recent calculations on the photodisintegration of spheroidal nuclei. In qualitative agreement with these calculations, it was found that the (γ,n) cross sections for the other distorted nuclei investigated, 150Nd, 154Sm and 160Gd, have widths of 5.7, 6.5 and 5.3 MeV respectively, while for the closed-shell nuclei 141Pr, 142Nd and 144Sm, the corresponding (γ,n) cross sections have widths of 4.3, less than 5.0 and 4.0 MeV. In addition, it was found that the (γ,n) cross sections for closed-shell nuclei have substantially larger high-energy tails than do those for spheroidal nuclei.