Weisskopf Units Research Articles

Investigation of octupole collectivity near the A=72 shape-transitional point

Enhanced octupole collectivity is expected in the neutron-deficient Ge, Se and Kr isotopes with neutron number $N \approx 40$ and has indeed been observed for $^{70,72}$Ge. Shape coexistence and configuration mixing are, however, a notorious challenge for theoretical models trying to reliably predict octupole collectivity in this mass region, which is known to feature rapid shape changes with changing nucleon number and spin of the system. To further investigate the microscopic configurations causing the prolate-oblate-triaxial shape transition at $A \approx 72$ and their influence on octupole collectivity, the rare isotopes $^{72}$Se and $^{74,76}$Kr were studied via inelastic proton scattering in inverse kinematics. While significantly enhanced octupole strength of $\sim 32$ Weisskopf units (W.u.) was observed for $^{72}$Se, only strengths of $\sim 15$ W.u. were observed for $^{74,76}$Kr. In combination with existing data, the new data clearly question a simple origin of enhanced octupole strengths around $N = 40$. The present work establishes two regions of distinct octupole strengths with a sudden strength increase around the $A=72$ shape transitional point.

Neutron-proton pair transfer reactions and corresponding Weisskopf-type units

We introduce the concept of neutron-proton two-particle units (np-Weisskopf units) to be used in the analysis of the (3He,p) and (p,3He) reactions on nuclei along the N=Z line. These are presented for the conditions relevant to the (n,j,ℓ) orbits expected from 16O to 100Sn. As is the case of the Weisskopf units for electromagnetic transitions, the np-WU's will provide a simple, yet robust, measure of isoscalar and isovector np pairing collective effects.

Alpha decay measured in single-particle units as a manifestation of nuclear collectivity

A salient feature of quantum mechanics is the inherent property of collective quantum motion, when apparent independent quasiparticles move in highly correlated trajectories, resulting in strongly enhanced transition probabilities. To assess the extend of a collective quantity requires an appropriate definition of the uncorrelated average motion, often expressed by single particle units. A well known example in nuclear physics is the Weisskopf unit for electromagnetic transitions which reveals different aspects of collective motion. In this paper we define the corresponding single particle unit for alpha decay as induced by four uncorrelated/non-interacting protons and neutrons. Our definition facilitates an unified description of all alpha decay processes along the nuclear chart, revealing a simple mass dependence. The comparison of the uncorrelated decay rates with the experimentally observed ones, shows a significant enhancement of the decay rates pointing towards collective alpha like correlations in the nuclear ground state. As a limiting case, the formalism presented here is applied to proton decay revealing its single particle nature.

Yrast band in the heavy N = Z nucleus ^{88}Ru: alpha -cluster approach

The yrast band in the heavy N = Z nucleus ^{88}Ru is studied in the framework of the alpha -cluster model in combination with double-folding potentials. It is found that the excitation energies of the yrast band in ^{88}Ru can be nicely described within the alpha -cluster approach using a smooth and mildly L-dependent adjustment of the potential strength. This result is similar to well-established alpha -cluster states in nuclei with a (magic core otimes alpha ) structure. Contrary, the yrast bands in neighboring N ne Z nuclei deviate from such a typical alpha -cluster behavior. Finally, the alpha -cluster model predicts reduced transition strengths of about 10 Weisskopf units for intraband transitions between low-lying states in the yrast band of ^{88}Ru.

Two-neutron and core-excited states in Pb210 : Tracing E3 collectivity and evidence for a new β -decaying isomer in Tl210

Yrast and near-yrast levels up to an I=17ℏ spin value and a 6-MeV excitation energy have been delineated in the “two-neutron” 210Pb nucleus following deep-inelastic reactions involving 208Pb targets and a number of heavy-ion beams at energies ∼25% above the Coulomb barrier. The level scheme was established on the basis of multifold prompt and delayed coincidence relationships measured with the Gammasphere array. In addition to the previously known states, many new levels were identified. For most of the strongly populated states, spin-parity assignments are proposed on the basis of angular distributions. The reinvestigation of the ν(g9/2)2, 8+ isomeric decay results in the firm identification of the low-energy E2 transitions involved in the 8+→6+→4+ cascade, and in a revised 6+ level half-life of 92(10) ns, nearly a factor of 2 longer than previously measured. Among the newly identified states figure spin I=4–10ℏ levels associated with the νg9/2i11/2 multiplet, as well as yrast states involving νg9/2j15/2, νi11/2j15/2, and ν(j15/2)2 neutron couplings. The highest-spin excitations are understood as 1p−1h core excitations and the yrast population is found to be fragmented to the extent that levels of spin higher than I=17ℏ could not be reached. Four E3 transitions are present in the 210Pb yrast decay; three of these involve the g9/2→j15/2 octupole component, as reflected in the 21(2) and >10 Weisskopf unit enhancements of the B(E3) rates of the first two. The fourth, 16+→13−E3 transition corresponds to the 3− core octupole excitation built on the νi11/2j15/2 state, in analogy to a similar E3 coupling to the νj15/2 level in 209Pb. Shell-model calculations performed for two-neutron states and 1p−1h 208Pb core excitations are in good agreement with the data. Evidence was found for the existence of a hitherto unknown high-spin β-decaying isomer in 210Tl. Shell-model calculations of the 210Tl levels suggest the possibility of a 11+ long-lived, β-decaying state, and the delayed yields observed in various reactions fit rather well with a 210Tl assignment.

Halo-induced large enhancement of soft dipole excitation of 11Li observed via proton inelastic scattering

Proton inelastic scattering off a neutron halo nucleus, 11Li, has been studied in inverse kinematics at the IRIS facility at TRIUMF. The aim was to establish a soft dipole resonance and to obtain its dipole strength. Using a high quality 66 MeV 11Li beam, a strongly populated excited state in 11Li was observed at Ex=0.80±0.02 MeV with a width of Γ=1.15±0.06 MeV. A DWBA (distorted-wave Born approximation) analysis of the measured differential cross section with isoscalar macroscopic form factors leads us to conclude that this observed state is excited in an electric dipole (E1) transition. Under the assumption of isoscalar E1 transitions, the strength is evaluated to be extremely large amounting to 30∼296 Weisskopf units, exhausting 2.2%∼21% of the isoscalar E1 energy-weighted sum rule (EWSR) value. The large observed strength originates from the halo and is consistent with the simple di-neutron model of 11Li halo.

Multifaceted Quadruplet of Low-Lying Spin-Zero States in ^{66}Ni: Emergence of Shape Isomerism in Light Nuclei.

A search for shape isomers in the ^{66}Ni nucleus was performed, following old suggestions of various mean-field models and recent ones, based on state-of-the-art MonteCarlo shell model (MCSM), all considering ^{66}Ni as the lightest nuclear system with shape isomerism. By employing the two-neutron transfer reaction induced by an ^{18}O beam on a ^{64}Ni target, at the sub-Coulomb barrier energy of 39MeV, all three lowest-excited 0^{+} states in ^{66}Ni were populated and their γ decay was observed by γ-coincidence technique. The 0^{+} states lifetimes were assessed with the plunger method, yielding for the 0_{2}^{+}, 0_{3}^{+}, and 0_{4}^{+} decay to the 2_{1}^{+} state the B(E2) values of 4.3, 0.1, and 0.2 Weisskopf units (W.u.), respectively. MCSM calculations correctly predict the existence of all three excited 0^{+} states, pointing to the oblate, spherical, and prolate nature of the consecutive excitations. In addition, they account for the hindrance of the E2 decay from the prolate 0_{4}^{+} to the spherical 2_{1}^{+} state, although overestimating its value. This result makes ^{66}Ni a unique nuclear system, apart from ^{236,238}U, in which a retarded γ transition from a 0^{+} deformed state to a spherical configuration is observed, resembling a shape-isomerlike behavior.

Lifetime measurements in Dy162

Background: The nature of oscillations or excitations around the equilibrium deformed nuclear shape remains an open question in nuclear structure. The $^{162}\mathrm{Dy}$ nucleus is one of the most extensively studied nuclei with the $(n,\ensuremath{\gamma})$, $(n,{e}^{\ensuremath{-}})$, $(\ensuremath{\alpha},2n)$ reactions and most recently the $(p,t)$ pickup reaction adding 11 ${0}^{+}$ states to an excitation energy of 2.8 MeV to an already-well-developed level scheme. However, a major shortfall for a better understanding of the nature of the plethora of bands and levels in this nucleus has been the lack of lifetime measurements.Purpose: To determine the character of the low-lying excited bands in this $^{162}\mathrm{Dy}$ nucleus, we set out to measure the level lifetimes.Method: Lifetimes were measured in the $^{162}\mathrm{Dy}$ nucleus following neutron capture using the Gamma-Ray-Induced Doppler (GRID) broadening technique at the Institut Laue-Langevin in Grenoble, France.Results: In total, we have measured the lifetimes of 12 levels belonging to a number of excited positive- and negative-parity bands in the low-lying spectrum of the $^{162}\mathrm{Dy}$ nucleus. The lifetime of the ${K}^{\ensuremath{\pi}}={2}^{+}$ bandhead at 888.16 keV was previously measured. We confirm this value and measure lifetimes of the ${3}^{+}$ and ${4}^{+}$ members of this band yielding $B(E2)$ values that are consistent with a single $\ensuremath{\gamma}$-vibrational phonon of several Weisskopf units. The first excited ${K}^{\ensuremath{\pi}}={4}^{+}$ band, with a bandhead at 1535.66 keV, is strongly connected to the ${K}^{\ensuremath{\pi}}={2}^{+}$ band with enhanced collective $B(E2)$ values and it is consistent with a double phonon vibrational $(\ensuremath{\gamma}\ensuremath{\gamma})$ excitation. Lifetime of ${K}^{\ensuremath{\pi}}={0}^{+}$ band members have also been measured, including the ${4}_{{K}^{\ensuremath{\pi}}={0}_{2}^{+}}^{+}$ state at 1574.29 keV and the ${2}_{{K}^{\ensuremath{\pi}}={0}_{3}^{+}}^{+}$ state at 1728.31 keV. This latter state also displays the characteristics of a double phonon excitation built on the ${K}^{\ensuremath{\pi}}={2}^{+}$ band.Conclusions: We discuss our findings in terms of the presence or absence of collective quadrupole and octupole vibrational excitations. We find two positive-parity excited bands at 1535.66 keV $({K}^{\ensuremath{\pi}}={4}^{+})$ and the 1728.312-keV ${2}^{+}$ state of a ${K}^{\ensuremath{\pi}}={0}^{+}$ band at 1666 keV connected with sizably collective $B(E2)$ values to the $({K}^{\ensuremath{\pi}}={2}^{+})\phantom{\rule{0.16em}{0ex}}\ensuremath{\gamma}$ band at 888 keV.

Isomeric Character of the Lowest Observed 4+ State in S44

Previous experiments observed a 4^{+} state in the N=28 nucleus ^{44}S and suggested that this state may exhibit a hindered E2-decay rate, inconsistent with being a member of the collective ground state band. We populate this state via two-proton knockout from a beam of exotic ^{46}Ar projectiles and measure its lifetime using the recoil distance method with the GRETINA γ-ray spectrometer. The result, 76(14)_{stat}(20)_{syst} ps, implies a hindered transition of B(E2;4^{+}→2_{1}^{+})=0.61(19) single-particle or Weisskopf units strength and supports the interpretation of the 4^{+} state as a K=4 isomer, the first example of a high-K isomer in a nucleus of such low mass.

Pairing effect and misleading regularity

We study the nearest neighbor spacing distribution of energy levels of even–even nuclei classified according to their reduced electric quadrupole transition probability B(E2)↑ using the available experimental data. We compare between Brody, and Abul-Magd distributions that extract the degree of chaoticity within nuclear dynamics. The results show that Abul-Magd parameter f can represents the chaotic behavior in more acceptable way than Brody, especially if a statistically significant study is desired. A smooth transition from chaos to order is observed as B(E2)↑ increases. An apparent regularity was located at the second interval, namely: at 0.05≤B(E2)<0.1 in e2b2 units, and at 10≤B(E2)<15 in Weisskopf unit. Finally, the chaotic behavior parameterized in terms of B(E2)↑ does not depend on the unit used.

Lifetime measurement for the21+state inSm140and the onset of collectivity in neutron-deficient Sm isotopes

Background: The chain of Sm isotopes exhibits a wide range of nuclear shapes and collective behavior. While the onset of deformation for $Ng82$ has been well studied both experimentally and theoretically, fundamental data is lacking for some Sm isotopes with $Nl82$.Purpose: Electromagnetic transition rates represent a sensitive test of theoretical nuclear structure models. Lifetime measurements are furthermore complementary to Coulomb excitation experiments, and the two methods together can give access to spectroscopic quadrupole moments.Method: The lifetime of the ${2}_{1}^{+}$ state in $^{140}\mathrm{Sm}$ was measured with the recoil-distance Doppler shift technique using the reaction $^{124}\mathrm{Te}(^{20}\mathrm{Ne},4\mathrm{n})^{140}\mathrm{Sm}$ at 82 MeV. Theoretical calculations were performed based on a mapped collective Hamiltonian in five quadrupole coordinates (5DCH) and the Gogny D1S interaction.Results: The lifetime of the ${2}_{1}^{+}$ state in $^{140}\mathrm{Sm}$ was found to be 9.1(6) ps, corresponding to a $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ value of 51(4) Weisskopf units. The theoretical calculations are in very good agreement with the experimental result.Conclusions: The $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ value for $^{140}\mathrm{Sm}$ fits smoothly into the systematic trend for the chain of Sm isotopes. The new beyond-mean field calculations are able to correctly describe the onset of collectivity in the Sm isotopes below the $N=82$ shell closure for the first time.

Study of Electromagnetic Multipole Transition Half-Lives of One-Hole 15O–15N and One-Particle 17O–17F Mirror Nuclei

Energy spectrum and wave functions are obtained numerically with a potential consisting of Woods-Saxon, Coulomb, and spin-orbit coupling parts for the nuclei 15O, 15N, 17O, and 17F. The radial parts of the wave functions are used to calculate some matrix elements of electromagnetic transitions. These results are applied to calculate half-lives of low-lying exited states in the one-particle 17O and 17F as well as in the one-hole 15O and 15N isotopes. The calculated half-lives are compared with available experimental and theoretical results based on harmonic oscillator wave functions and Weisskopf units. In comparison with the results calculated from the other methods, our results based on the Woods-Saxon potential indicate a satisfactory agreement with accessible experimental data.

Breakup Reactions of Neutron Drip Line Nuclei Near N=20

Coulomb breakup at intermediate energies is a useful experimental tool for investigating the microscopic structure of neutron drip-line nuclei. Here, results from the inclusive Coulomb breakup experiment of 31Ne on a lead target at RIBF(RI Beam Factory) at RIKEN are presented. The experiment was performed as one of day-one campaign experiments at RIBF, using a 48Ca primary beam at 345 MeV/nucleon. A unique feature of a halo nucleus is the enhanced electric dipole strength of the order of 1 W.u.(Weisskopf unit) at very low excitation energies around 1 MeV (soft E1 excitation). Owing to high sensitivity of the Coulomb breakup to the soft E1 excitation, a measurement of inclusive Coulomb breakup cross section can be used to identify the halo structure of a certain drip-line nucleus. We have indeed observed a strong enhancement of the Coulomb breakup cross section of 540(70) mb for 31Ne on Pb at 230 MeV/nucleon, nearly as high as that for the known halo nucleus 19C, thereby giving evidence of the halo structure in 31Ne. The finding of a new halo structure for such a heavy system, compared to the known halo nuclei, is the first step for the understanding of halo phenomena along the neutron drip line towards heavier nuclei. We discuss also the change of shell structure in 31Ne, as a nucleus in the island of inversion.

Ultrahigh-Resolutionγ-Ray Spectroscopy ofGd156: A Test of Tetrahedral Symmetry

Tetrahedral symmetry in strongly interacting systems would establish a new class of quantum effects at subatomic scale. Excited states in 156Gd that could carry the information about the tetrahedral symmetry were populated in the 155Gd(n,γ)156Gd reaction and studied using the GAMS4/5 Bragg spectrometers at the Institut Laue-Langevin. We have identified the 5(1)- → 3(1)- transition of 131.983(12) keV in 156Gd and determined its intensity to be 1.9(3)x10(-6) per neutron capture. The lifetime τ=220(-30)(+180) fs of the 5(1)- state in 156Gd has been measured using the GRID technique. The resulting B(E2)=293(-134)(+6) Weisskopf unit rate of the 131.983 keV transition provides the intrinsic quadrupole moment of the 5(1)- state in 156Gd to be Q0=7.1(-1.6)(+0.7) b. This large value, comparable to the quadrupole moment of the ground state in 156Gd, gives strong evidence against tetrahedral symmetry in the lowest odd-spin, negative-parity band of 156Gd.

Observation/confirmation of hindered E2 strength in 18C/16C

We have measured the lifetime of the first excited 2+ state in 18C using an upgraded recoil shadow method to determine the electric quadrupole transition. The measured mean lifetime is 18.9±0.9 (stat)±4.4 (syst) ps, corresponding to B(E2;21 + \( \rightarrow\) 0+ gs) = 4.3±0.2±1.0e 2 fm^4, or about 1.5 Weisskopf units. The mean lifetime of the first 2+ state in 16C was remeasured to be 18.3±1.4±4.8 ps, about four times shorter than the value reported previously. The discrepancy is explained by incorporating the \( \gamma\) -ray angular distribution obtained in this work into the previous measurement. The observed transition strengths in 16, 18C are hindered compared to the empirical values, indicating that the anomalous E2 strength observed in 16C persists in 18C .

Low-Lying Neutron Intruder State inB13and the Fading of theN=8Shell Closure

A lifetime measurement of the excited states in the neutron-rich isotope (13)B has been performed using the (7)Li((7)Li,p)(13)B reaction. An anomalously long mean lifetime of 1.3(3) ps was found for the excited state at 3.53 MeV, giving the upper limits of the transition strengths to the ground state: B(M1) = 7.2 x 10;{-4} Weisskopf unit (W.u.) and B(E2) = 0.81 W.u.. The hindered transition strengths indicate significant intruder configurations for the excited state, coexisting with the normal ground state. The data are well explained by recent shell-model calculations, which suggest J;{pi} = 3/2;{-} for the 3.53-MeV state with the dominant intruder (nu2p2h) configuration.

ANOMALOUSLY HINDERED E2 STRENGTHS IN 16,18C

Lifetime measurement of the first excited 2+ state in 18 C was performed using an upgraded recoil shadow method to determine the electric quadrupole transition. The measured mean lifetime is 18.9 ± 0.9 (stat) ± 4.4 (syst) ps, which corresponds to a [Formula: see text] value of 4.3 ± 0.2 ± 1.0 e2 fm 4, or about 1.5 Weisskopf units. The mean lifetime of the first 2+ state in 16 C was remeasured to be about 18 ps, about four times shorter than the value reported previously. By incorporating the γ-ray angular distribution measured in this work into the previous measurement, this discrepancy has been explained. The observed transition strengths in 16,18 C are hindered compared to the empirical transition strengths, indicating that the anomalous hindered E2 strength observed in 16 C persists in 18 C .

First lifetime measurement of [formula omitted] state in 12Be

The lifetime of the 21+ state at 2.1 MeV in 12Be has been measured using inelastic scattering of a 12Be beam at 43 MeV/nucleon with a gold target. Through the Doppler shift attenuation method, the mean-life of the 21+ state has been determined as 2.5±0.7 (stat) ±0.3 (syst) ps, which gives a B(E2;21+→0g.s.+) value of 4.9±1.3±0.5 in Weisskopf units. The result shows a large quadrupole strength in the ground state transition, providing further evidence on the disappearance of the N=8 magic number. The B(E2;21+→0g.s.+) value together with the deformation length measured by proton inelastic scattering yields a neutron quadrupole matrix element two times larger than those for 14C and 16O.

Lifetime measurements of first excited states inC16,18

The electric quadrupole transition from the first 2{sup +} state to the ground 0{sup +} state in {sup 18}C was studied through a lifetime measurement by an upgraded recoil shadow method applied to inelastically scattered radioactive {sup 18}C nuclei. The measured mean lifetime is 18.9{+-}0.9(stat){+-}4.4(syst) ps, corresponding to a B(E2;2{sub 1}{sup +}{yields}0{sub g.s.}{sup +}) value of 4.3{+-}0.2{+-}1.0 e{sup 2} fm{sup 4}, or about 1.5 Weisskopf units. The mean lifetime of the first 2{sup +} state in {sup 16}C was remeasured to be 18.3{+-}1.4{+-}4.8 ps, about four times shorter than the value reported previously. The discrepancy between the two results was explained by incorporating the {gamma}-ray angular distribution measured in this work into the previous measurement. These transition strengths are hindered compared to the empirical transition strengths, indicating that the anomalous hindrance observed in {sup 16}C persists in {sup 18}C.

Soft E1 excitation of neutron-halo nuclei

Soft electric dipole (E1) response of 11 Li has been investigated by a kinematical complete measurement of the Coulomb breakup at about 70 MeV/nucleon. A two-wall neutron detector setup allowed us to employ a kinematical condition to exclude fully the cross talk events even for the low relative energies ( E rel ) down to 0 MeV, thereby enhancing the experimental sensitivities in this energy region. In the E rel spectrum, a strong peak corresponding to the soft E1 excitation has been observed at about E x = 0.6 MeV with B ( E1 ) = 1.42 ( 18 ) e 2 fm 2 (4.5(6) Weisskopf units) for 0 ⩽ E rel ⩽ 3 MeV . The spectral shape as well as its amplitude is in excellent agreement with a three-body model with strong neutron-neutron correlation in the halo. Such correlation is further supported by the E1 non-energy weighted cluster sum rule.