Excited States Of Even-even Nuclei Research Articles

Unified description of electromagnetic andαtransitions in even-even nuclei

We describe electromagnetic and $\ensuremath{\alpha}$-decay transitions to low-lying excited states in even-even nuclei within the coherent state model (CSM). We reproduced the energies and $B(E2)$ values for ground state bands in 40 daughter nuclei with known $\ensuremath{\alpha}$-branching ratios to ${2}^{+}$ states. To this purpose we used two parameters, namely the deformation parameter and the strength of the harmonic CSM Hamiltonian. The Hamiltonian describing the $\ensuremath{\alpha}$-emission process is given by two terms. The first term describes the dynamics of the daughter nucleus. The second $\ensuremath{\alpha}$-daughter component contains the monopole potential, estimated within the double folding procedure with M3Y interaction plus a repulsive core simulating Pauli principle and a quadrupole-quadrupole (QQ) interaction. The decaying states are identified with the lowest narrow outgoing resonances in this potential. The $\ensuremath{\alpha}$-branching ratios to ${2}^{+}$ states were reproduced by using the QQ strength depending linearly on the deformation parameter, as predicted by CSM. The theoretical intensities to ${4}^{+}$ and ${6}^{+}$ states are in a reasonable agreement with available experimental data. We found out that the QQ coupling strength is by one order of magnitude larger in the region above ${}^{208}$Pb, where the $\ensuremath{\alpha}$ clustering is known to be stronger, in comparison to other nuclei. This formalism is able to simultaneously describe electromagnetic and $\ensuremath{\alpha}$ decays to excited states in spherical, transitional, and well deformed nuclei.

Investigation of two-hole excited states and the pairing nucleon’s energies of even-even nuclei

In the framework of the adiabatic three-particle model of nuclei is given a theoretical description of the stationary states of spherical (deformed) even-even nuclei taking into account the strong nuclear and electromagnetic interactions. In particular, we study the nucleon pairing energy and the energy spectra of two-hole excited states of even-even nuclei in which to fill the outer shell are missed two protons. The efficiency of the model is illustrated by numerical calculations for even-even argon and ferrum isotopes. Key words: adiabatic three-particle model, Schrodinger’s equation, angular and radial correlations of nucleons, even-even nuclei, pairing energy.

A panorama of excited-state g-factor measurements: advancing moment measurements on radioactive beams

Patterns in the systematics of g factors for the first excited states of even-even nuclei are explored across the nuclear landscape for heavy nuclei (A > 90). The pathway to collectivity from semimagic to mid-shell nuclei is discussed, and attention given to the different behavior of nuclei either side of N = 82. As most g(2+1) data is for nuclides near the valley of stability, the development of the recoil in vacuum technique for moment measurements on radioactive beams is discussed,with particular attention given to the free-ion hyperfine fields of Se and Ge ions leaving carbon foils with velocities of about 5% of the speed of light.

Properties of $ \alpha$ -decay to ground and excited states of heavy nuclei

Branching ratios and half-lives of α-decay to the ground-state rotational bands as well as the high-lying excited states of even-even nuclei have been calculated in the framework of the generalized liquid drop model (GLDM) and Royer's formula that we improved very recently. The calculation covers the isotopic chains from Ra to No in the mass regions 222 ≤ A ≤ 252 and 88 ≤ Z ≤ 102. The agreement between the calculated results and the experimental data indicates the reliability of investigating the properties of the unfavored α-decay with our method, especially the improved Royer's formula, which is very valuable for the analysis of experimental data. In addition, the dependence of half-lives on excitation energies of daughter nuclei has been investigated. It is shown that the influence on half-lives becomes stronger and stronger with the increase of the excitation energies.

Branching ratios ofαdecay to excited states of even-even nuclei

Branching ratios of $\ensuremath{\alpha}$ decay to members of the ground state rotational band and excited ${0}^{+}$ states of even-even nuclei are calculated in the framework of the generalized liquid drop model (GLDM) by taking into account the angular momentum of the $\ensuremath{\alpha}$ particle and the excitation probability of the daughter nucleus. The calculation covers isotopic chains from Hg to Fm in the mass regions $180lAl202$ and $A\ensuremath{\geqslant}224$. The calculated branching ratios of the $\ensuremath{\alpha}$ transitions are in good agreement with the experimental data and some useful predictions are provided for future experiments.

Staggering behavior of the low-lying excited states of even-even nuclei in aSp(4,R)classification scheme

We implement a high order discrete derivative analysis of the low lying collective energies of even-even nuclei with respect to the total number of valence nucleon pairs N in the framework of F- spin multiplets appearing in a symplectic sp(4,R) classification scheme. We find that for the nuclei of any given F- multiplet the respective experimental energies exhibit a Delta N=2 staggering behavior and for the nuclei of two united neighboring F- multiplets well pronounced Delta N=1 staggering patterns are observed. Those effects have been reproduced successfully through a generalized sp(4,R) model energy expression and explained in terms of the step-like changes in collective modes within the F- multiplets and the alternation of the F-spin projection in the united neighboring multiplets. On this basis we suggest that the observed Delta N=2 and Delta N=1 staggering effects carry detailed information about the respective systematic manifestation of both high order alpha - particle like quartetting of nucleons and proton (neutron) pairing interaction in nuclei.PACS number(s):21.10.Re, 21.60.Fw

Properties of the low-lying excited states in even-even nuclei around the closed shell N=82

The properties of low-lying states in 136Ba and 144Nd are calculated within the quasiparticle phonon model. It is shown that the strong quadrupole interaction in the particle-particle channel leads to the appearance of low-lying isovector excitations. Due to this reason, there are two branches in the lowlying part of the spectrum, an isoscalar and an isovector one. Both branches show peculiar regularities of E2 and M1 transitions.

Hexadecapole reorientation in Coulomb excitation

The possibility of measuring static hexadecapole moments of nuclei is canvassed. Attention is restricted to hexadecapole moments of first excited states of even-even nuclei. Two schemes of measurement are explored. Both suffer from problems which make their implementation difficult.

Sum-rule approach to the static quadrupole moments of arbitrary excited states in even-even nuclei

Sum-rule approach to the static quadrupole moments of arbitrary excited states in even-even nuclei

Sum-rule approach to the static quadrupole moments of arbitrary excited states in even-even nuclei

The electronuclear sum-rule approach to static quadrupole moments is generalized to apply to arbitrary states in even nuclei. Additional results on the 2 1 + and 2 2 + states are reported and results for the 4 1 + states of 152Sm, 162Dy and 194Pt are given, and reasonable agreement with experiment is obtained. The sum-rule prediction of Q(3 1 −) for 194Pt remains to be tested.

A method of angular momentum projection for excited states in even-even nuclei

A method of angular momentum projection for the excited states in even-even nuclei is formulated within the framework of the Hartree-Bogoliubov theory. A preliminary application of this method is performed for the K=0 − band in 162Er.

A Collective Rotational State of Spherical Nuclei

We consider a particular many-body rotational excitation 'P of a spherical self-bound system of particles, of the form studied by Lekner (1974). This angular momentum eigenstate is translationally invariant and thus is not a spurious state. The energy of 'P is found from first principles to be substantially larger than that of the first 2+ excited states of even-even nuclei, with the exception of 208Pb. The quadrupole moment is negative, the g-factor is approximately Z/A and the lifetime is shorter than the single-particle (Weisskopf) value by a factor of the order of A/Z2. It is suggested that these states are the finite system rotational analogues of Feynman's phonons and rotons.

Alternative Iongitudinal coordinations of the excited states in even-even nuclei

The aim of the present letter is to show that there exist two different longitudinal coordinations of the collective vibrational levels built on several quadrupoles phonons ($d$ bosons). The first one reproduces that given earlier by Saka\ifmmode \check{i}\else \v{i}\fi{}. The second one explains and generalizes the $X$, $Y$, $Z$, ${X}^{\ensuremath{'}}$, ${Z}^{\ensuremath{'}}$, $\ensuremath{\beta}$, and $\ensuremath{\Delta}$ bands recently introduced by Iachello and Arima.NUCLEAR STRUCTURE Classification of excited states in even-even nuclei.

Investigation of neutron deficient nuclei in the region 28<N, Z <50 with the help of heavy ion compound reactions

In-beamγ ray spectroscopy withγ singles spectra,γγ coincidences andγ ray angular distributions has been performed with several target-projectile combinations:natCa +32S,natCa +40Ca,54Fe +14N,58Ni +12C,58Ni +14N,66Zn +16O,68Zn +16O. Level schemes of66Ge,68Ge,69As,70Se,74Kr,80Sr and82Sr have been deduced. The following level energies and spin-parity assignments have been found:66Ge: 957.4 keV, 2+; 1693.7; 2174.7, (4+); 3685.7; 4207.5;68Ge: 1015.8, 2+; 1777.9, 2+; 2267.9, 4+; 2428.8, 3(+); 2649.1, 3−; 3582.3, (5−); 3649.3, (5−); 3696.2, (6+); 3883.3, (6−); 4054.4, (7−); 4454.6; 4837.3;69As: 98.2; 164.6;789.6;863.2; 1306;2160;2210.4;2831.5;3258.3;3263.5;3991.1;5195.7;70Se: 945.4, 2+; 1600.9; 2039.4, (4+);74Kr: 455.7, 2+; 1013.5, (4+); 1781.5;80Sr: 385.4, 2+; 980.2, (4+); 1763.2, (6+);82Sr: 573.4, 2+; 1328.5,(4+); 2229.6,(6+). γ ray activity spectra have been measured after the bombardment of natural Ca with32S. The half-life of the new isotope69Se has been found to be 27±3 sec. Recoil distance Doppler-shift measurements have been performed with the reactions62,64Ni,66zn(16O, 2n)76, 78 Kr,80Sr. The following half-lives have been determined:76Kr: 423.8 keV, 2+, 37±5 psec; 1034.2,4+, 5.7±1.6;78Kr: 455.3, 2+, 25±3; 1120.0, 4+, 3.8±1;80Sr: 385.4, 2+, 44±6. The energy and half-life systematics of the first excited state of even-even nuclei suggest a maximum of nuclear deformation in the region 28≦N, Z≦50 near 38 76 Sr38 or 40 78 Zr38.

Transition probabilities and static moments of excited states in even-even nuclei

A new approach is made to calculate the generalized single-particle density matrixpμv in even-even nuclei. It is shown that this quantity is included in the three particle response function, for which we derived a renormalized equation. Taking into account in a consequent way the effective particle-hole interaction we received a formula for the static moment of excited states and the transition probability between such states which is essentially different from the usual RPA theory.

ORBITING CLUSTERS IN ATOMIC NUCLEI

As an alternative to their description as vibrational levels, the low excited states of even-even nuclei can be described as rotational states of a helion, dineutron, diproton, or other cluster about the rest of the nucleus, leading to reasonable values of the average distance between centers of the clusters. Some states involve rotational excitation of two or more helions or other clusters. The nature of the rotating clusters is determined by the relation of the neutron and proton numbers to the magic numbers.

Study of Second Excited2+States of Some Even-Even Nuclei by Beta-Gamma Angular Correlations

Beta-gamma directional correlations of several first-forbidden $\ensuremath{\beta}$ transitions leading to second excited states of even-even nuclei (${\ensuremath{\beta}}_{2}$ transitions) have been studied. The energy-dependence of the $\ensuremath{\beta}$ directional correlation factor ${A}_{2}(\ensuremath{\beta})$ in the $\ensuremath{\beta}\ensuremath{-}\ensuremath{\gamma}$ correlation function $W(\ensuremath{\theta})=1+{A}_{2}(\ensuremath{\beta}){A}_{2}(\ensuremath{\gamma}){P}_{2}(cos\ensuremath{\theta})$ has been measured for the ${\ensuremath{\beta}}_{2}$ transitions of ${\mathrm{As}}^{76}$, ${\mathrm{Sb}}^{122}$, ${\mathrm{I}}^{126}$, ${\mathrm{Sb}}^{124}$, and ${\mathrm{La}}^{140}$, and the reduced $\ensuremath{\beta}$ coefficient ${R}_{2}(W)=\frac{{A}_{2}(\ensuremath{\beta})}{(\frac{{\ensuremath{\lambda}}_{2}{p}^{2}}{W})}$ was determined. In all cases ${R}_{2}(W)$ was found to be very different from ${R}_{1}(W)$, the reduced $\ensuremath{\beta}$ factor describing the ${\ensuremath{\beta}}_{1}$ transition to the first excited state of the daughter nucleus. The results indicate that the relative magnitudes of the nuclear $\ensuremath{\beta}$-matrix elements in the ${\ensuremath{\beta}}_{1}$ transition and in the ${\ensuremath{\beta}}_{2}$ transition are significantly different, although the $\mathrm{ft}$ values are very similar. The implication of these experimental results for the structure of first and second excited states of even-even spherical nuclei is discussed.

THE INFLUENCES OF PAIRING FORCE ON THE PROPERTIES OF RARE-EARTH NUCLEI

In this paper the various properties of the rare-earth even-even nuclei (intrinsic excitation spectra, β-decay, and even-odd mass differences, etc.) are analysed with the new method presented in reference [10]. For this purpose, the single-particle levels have to be determined. It is found that on the basis of Nilsson's level scheme, with suitably chosen parameters μ and k, the spins and parities of the low-lying intrinsic spectra and the level spacing of odd-A nuclei may be explained, after taking account of the influence of pairing force. The parameters chosen are as follow: k～0.067-0.072, η～4-4.6 μ～0.59(N = 4), μ～0.45(N = 5) for proton μ～0.40-0.45(N = 5), μ～0.33(N = 6) for neutron. The variation of the energy eigenvalue induced by the change of parameter μ is estimated with the perturbation method, and the results are close to the exact eigenvalues. From the analyses of Er 166 , Er 168 , Yb 170 , Yb 172 , Yb 174 , Hf 178 , W 182 , Dy 160 and Dy 162 the following several conclusions may be drawn: 1. The majority of the low-lying intrinsic excited states of even-even nuclei may be considered as the pair-broken excited states. The calculated first pair-broken states, in spite of the large variation in their spins and parities, are observed in experiments systematically (Fig. 30). Their excitation energies range from 1.2 MeV to 1.6 MeV. The calculated variation of these energies with different nuclei agrees with experiments ap- proximately. These states correspond to the two quasi-particle excited states pointed out by Gallagher and Soloviev.2. Near the first pair-broken excited state, appears the K π =0+ pair excitation state. In Er 166 , Hf 178 and W 182 these pair excitation states have been observed (Fig. 32). In other nuclei, these pair excitation states have not been observed yet, because the β-decays from the neighbouring odd-odd nuclei to these states are highly forbidden or strictly forbidden. 3. The systematically occured K π = 2+ states (Fig. 31) in even-even nuclei (E～0.8-1.2 MeV) can not be considered as pair-broken excited states. Theoretically there does not exist in these nuclei (except Yb 172 ) the K π = 2+ intrinsic state below 2 MeV. 4. The splittings in energy △E between the pair-broken doublets, K = |Ω 1 ± Ω 2 |, vary violently with different nuclei and with different pair-broken states. △E～(40-700) KeV. 5. The variation of even-odd mass differences with different nuclei is analysed also and it is found that the even-odd mass difference depends sensitively on the single-particle level scheme. The fact that the calculated and the observed variation of even-odd mass differences agree with each other (Fig. 29) indicates that the single-particle level scheme determined in this paper is approximately correct. The average strength constant G deduced from the even-odd mass differences is close to that deduced from the energy spectra. In the calculation the cut-off energy C is chosen to be ≈ 4 MeV. (C》G). With increasing C the influences of the pairing force on the low-lying spectra may be compensated by decreasing the average strength constant G.

Analysis of some allowed beta-transitions

Sakai’s method of analysing logft values has been extended to higher excited states in even-even nuclei. Within the context of the rather limited data an enhancement in the matrix element is observed for transitions to 2″+, 2‴+ and 4′+ and 4″+ levels.

Classification of excited states of even-even nuclei

In this paper we have attempted to see how far a classification of excited states of even-even nuclei can be made based on the quantity AE, A being the mass number and E, the energy of excitation. The results show that this may be a useful criterion in the understanding of the excitation mechanism.