Transition probabilities and hole-core coupled configurations in107In

The nucleus¹⁰⁷In was studied by in-beam spectroscopic methods in (HI, xn yp) reactions. Spin and parity values of some levels were determined by conversion electron andγ-ray measurements. Using the generalized centroid shift method, the half-lives T_1/2(19/2⁺, 2003.6 keV)=0.6±0.2 ns and T_1/2(17/2⁺, 1853.4 keV)=1.7±0.3 ns were measured. The systematics of the lowest members of the multipletπg ₉ ^2/?1 ×6 ₁ ⁺ in^111,109,107In is discussed     

Microscopic foundation of the interacting boson model in thes d-shell nuclei

Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to lights d-shell nuclei. The key ingredients of our approach are:a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure;b) two successive unitary transformations that extract the “maximally decoupled” collective bosons with angular momentaJ=0(s _ππ ⁺ ,s _νν ⁺ ,s _πν ⁺ ) andJ =2(d _ππ ⁺ ,d _νν ⁺ ,d _πν ⁺ (T=0),d _πν ⁺ (T=1)). The method is applied to obtain the low-energy spectra and the electron scattering form factors for the 0 ₁ ⁺ →2 ₁ ⁺ transitions in²⁰Ne and²⁴Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s _πν ⁺ ,d _πν ⁺ (T=1),d _πν ⁺ (T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.     

Properties of the 69 150 Tm81 6− β-decaying isomer

Decay experiments for¹⁴⁸Ho 6^? and¹⁵⁰Tm 6^? were carried out at the GSI On-line mass separator using 5 MeV/A⁵⁸Ni-beams on⁹⁴Mo and⁹⁶Ru targets. Gammaγ-andγX-coincidences established the¹⁵⁰Tm 6^? decay scheme, and e^? gave firm I ^π assignments for¹⁴⁸Dy and¹⁵⁰Er levels fed in the decays. It was found that the previously unknown 6 ₁ ^? state in¹⁵⁰Er receives significantβ-strength, which strongly suggestsπh _11/2 νs ₁ ^2/?1 character for the¹⁵⁰Tm 6^? isomer. The results are discussed in terms of the expected GT strength function. Shell model calculations for theπh ₁₁ ^2/4 yrast states are presented.     

Decays of millisecond isomers in odd-oddN=81 nuclei146Tb,148Ho and150Tm

Following reactions induced by 245 MeV⁶⁰Ni ions, isomers have been identified in the odd-oddN=81 isotones¹⁴⁶Tb,¹⁴⁸Ho and¹⁵⁰Tm with half-lives of 1.18(2), 2.35(4) and 5.2(3) ms, respectively. Their decays have been characterized byγ-ray spectroscopy. The isomers are interpreted as (πh _11/2 νh ₁ ^2/?1 ) 10⁺ states decaying to members ofπh _11/2 νd ₃ ^2/?1 andπh ₁₁ ^2/?1 multiplets. The observed level spectra and M1 branching ratios are found to be in good agreement with shell model predictions based on empirical and Schiffer-Trueπν ^?1 residual interactions.     

IsoscalarE2 transition strengths in 10≦A≦48 nuclei

Electric quadrupole transition strengths for the 2 ₁ ⁺ ,T=1→0 ₁ ⁺ ,T=1γ-decay branches are summarized for 10≦A≦42 nuclei. In¹⁰B the corresponding branch has been remeasured by use of the⁹Be(p, γ)¹⁰B resonance reaction atE _p =320 keV; an upper limit of 0.6% is found. The variation of theE2 strengths within each individualT=1 isobaric multiplet reveals the particleor hole-character of the levels involved. The isoscalar 2 ₁ ⁺ →0 ₁ ⁺ transition strengths in 10≦A≦48 nuclei vary between 2 and 20 Weißkopf units showing drastic shell effects. Results for the ratio of neutron and proton matrix elements deduced from analogγ-decay studies and from inelastic pion scattering are compared.     

Study of the decayf 1(1285)→ρ0(770)γ

The decayf ₁(1285)→ρ⁰(770)γ was studied at VES spectrometer of IHEP. Clear signal off ₁(1285) is seen in the effective mass spectrum of the π⁺π^?γ system in the reaction π^?γN→π⁺π^?π^?γN at the momentum $P_{\pi ^ - } = 37 GeV/c$ . The branching fraction of decayf ₁(1285)→ρ⁰(770)γ has been found to be $$BR(f_1 (1285) \to \rho ^0 (770)\gamma ) = (2.8 \pm 0.7(stat) \pm 0.6(syst)) \cdot 10^{ - 2} .$$ The ratio of the helicity amplitudes for ρ⁰ meson in its rest frame was determined by the analysis of angular distributions: $$\rho _{00} /\rho _{11} = 3.9 \pm 0.9(stat) \pm 1.0(syst).$$      

Transition probabilities and the structure of some negative-parity states in126,130Xe and132Ba

The lifetimes of several negative-parity states in^126,130Xe and¹³²Ba have been determined by means of the generalized centroid-shift method. The reactions^124,128Te(α,2n) and¹²²Sn(¹³C, 3n) have been used. Following results were obtained:T _1/2(2758 keV)=1.3±0.2 ns in¹²⁶Xe,T _1/2(2060 keV)=0.20±0.10 ns,T _1/2(2104 keV)=0.50±0.10 ns,T _1/2(2376 keV)=0.30±0.10 ns andT _1/2(2973 keV)=4.6±0.4 ns in¹³⁰Xe as well asT _1/2(2120 keV)=0.40 _?0.10 ^+0.20 ns in¹³²Ba. A systematics of the B(E2; 7 _? ¹ ?5 ₁ ^? ) values in theN=76 nuclei is presented. Electric dipole and quadrupole transition rates are discussed in terms of octupole and quadrupole collectivity. The structure of the 5 ₁ ^? and 7 ₁ ^? states is considered. Nuclear reactions:^124,128Te(α, 2 _n ),E=26 MeV,¹²²Sn (¹³C, 3n),E=53 MeV; measuredE _γ I _γ , γ-r.f. DeducedT _1/2, B(σL) in^126,130Xe and¹³²Ba. Ge detectors. Generalized centroid-shift analysis.     

Gyromagnetic ratios of excited states in186W

The gyromagnetic ratios of the 4 ₁ ⁺ , 6 ₁ ⁺ , and 2 ₂ ⁺ states in¹⁸⁶W were measured relative to that of the 2 ₁ ⁺ level by means of the transient field implantation perturbedγ-ray angular distribution technique. The nuclei in the states of interest were Coulomb excited using a beam of 220-MeV⁶³Cu projectiles and recoiled swiftly through a thin, polarized Fe foil. The present measurements yielded ratiosg(4 ₁ ⁺ )/g(2 ₁ ⁺ )=1.04±0.07,g(6 ₁ ⁺ )/g(2 ₁ ⁺ )=1.03 ±0.20 andg(2 ₂ ⁺ )/g(2 ₁ ⁺ )=0.63±0.13. The sizable disparity between the measuredg-factors of the ground- and excited-band is examined within the context of the interacting boson approximation model.     

The 235 ns 9+ isomer in 63 148 Eu85

From (p, xn) in-beamγ-ray and electron measurements aT _1/2=235(14) ns isomer at 720 keV was identified in ₆₃ ¹⁴⁸ Eu₈₅ and the levels populated in its decay have been characterized. The results determineI ^π=9⁺ for the isomeric state, and we assign it as the (πh _11/2 j ₀ ^?2 ν f ₇ ^2/3 )9⁺ shell model state, analogous to the configuration of the 235 μs isomer in ₆₃ ¹⁴⁶ Eu₈₃.     

Measurement of theg-factor of the 4 1 + -state of202Pb

Theg-factor of the 4 ₁ ⁺ -state of²⁰²Pb was investigated by the IPAC-technique. Inspite of the long half-life, which was measured as:T _1/2(4 ₁ ⁺ -state)=1.97(2)ns and the strong applied external magnetic field of 95.0 kG no rotation of the 787 keV-(422keV)-961 keVγ-γ angular correlation could be observed. Theg-factor must therefore be very small. A computer fit gave the limits:g(4 ₁ ⁺ -state)=+0.002(4). This smallg-factor can be understood by the assumption of an accidental cancellation of a positive contribution by the main [f _5/2 ² ]₄-configuration and several negative contributions by admixtures of all other possible two neutron configurations.     

Nuclear spin relaxation of Xe in liquid Te

By the method of time differential perturbed angular distribution following a nuclear reaction, the relaxation rateT _r ^?1 of the 8 msI ^π=10⁺ isomer of¹³²Xe has been measured in liquid Te. Between 670 °K (supercooled liquid) and 1,000 °K the rate decreases from about 720/s by about a factor of two. From existing experimental material it is concluded thatT _r ^?1 is mainly due to quadrupolar interaction (T _r ^?1 ≈T _Q ^?1 ). Its magnitude is discussed considering the metallic and the noble gas limit as models for the Xe-Te-interactions. The temperature dependenceT _Q(T) apparently does not correlate with the diffusion constant of Te in contrast to a simplified theoretical treatment. — The nuclearg value of the isomer has been determined to be g=(?)0.195(5) thus confirming the configuration (vh_11/2)².     

Hyperfine structure of EPR spectra of Gd3+ odd isotopes in PbMoO4, Pb5Ge3O11, YVO4, and quadrupole interaction (temperature dependence)

A hyperfine structure of EPR signals of odd isotopes Gd³⁺ in Pb₅Ge₃O₁₁, PbMoO₄, and YVO₄ single crystals has been investigated at different temperatures. The observation of forbidden (with the nuclear spin flip) transitions has made it possible to determine quadrupole interaction P ₂ ⁰ associated with the gradient of the electric field of ligands at the impurity. It has been shown for the first time that, under the condition |P ₂ ⁰ | ≥ |A _{x, y} | (A _i are the tensor components), not only the magnitudes of splitting but also the observed asymmetry in a hyperfine structure (in perpendicular orientations of the magnetic field) depends on mutual signs of parameters of initial splitting b ₂ ⁰ and P ₂ ⁰ . Results of studying the spectra have demonstrated that |b ₂ ⁰ (T)|/|P ₂ ⁰ (T)| ～ const for a concrete single crystal, which assumes the similarity of physical mechanisms determining these parameters.     

Transition probabilities and the structure of some negative-parity states in 126,130Xe and 132Ba

The lifetimes of several negative-parity states in ^126,130Xe and ¹³²Ba have been determined by means of the generalized centroid-shift method. The reactions ^124,128Te(α, 2n) and ¹²²Sn(¹³C, 3n) have been used. Following results were obtained: T_1/2(2758 keV) = 1.3 ± 0.2 ns in ¹²⁶Xe, T_1/2 (2060 keV) = 0.20 ± 0.10 ns, T_1/2 (2104 keV) = 0.50 ± 0.10 ns, T_1/2 (2376 keV) = 0.30 ± 0.10 ns and T_1/2 (2973 keV) = 4.6 ± 0.4 ns in ¹³⁰Xe as well as T _1/2(2120 keV) = 0.40 _?0.10 ^+0.20 ns in ¹³²Ba. A systematics of the B(E2; 7 ₁ ^? ? 5 ₁ ^? ) values in the N = 76 nuclei is presented. Electric dipole and quadrupole transition rates are discussed in terms of octupole and quadrupole collectivity. The structure of the 5 ₁ ^? and 7 ₁ ^? states is considered. Nuclear reactions: ^124,128Te(α, 2n), E = 26 MeV, ¹²²Sn (¹³C, 3n), E = 53 MeV; measured E_{gg}, I_{gg}, γ-r.f. Deduced T_1/2, B(σL) in ^126,130Xe and ¹³²Ba. Ge detectors. Generalized centroid-shift analysis.     

On the yrast levels in204Pb

High-spin states in²⁰⁴Pb were populated in the²⁰⁴Hg(α,4n) reaction using α-particles in the energy region 42–51 MeV. Prompt and delayedγ-rays as well as conversion electrons were studied in addition to excitation functions, angular distributions andγ-γ coincidences. In this way a stretched cascade ofγ-rays from a level at 8125.9 keV was found to feed the previously known isomeric 9^? level at 2185.7 keV. Spins and parities were established for levels up to and including a 19^? level at 6098.0 keV. The levels with c= 17^2212; and 19^? at excitation energies of 5664.3 and 6098.0 keV are likely to be due to the simplep ₁ ^2/s-1 i ₁₃ ^2/?3 andf ₅ ^2/?1 i ₁₃ ^2/?3 configurations. The agreement between calculated and experimental energies for all observed levels in the regionJ=9–19 is very good in cases where the empirical two-particle interactions used are satisfactorily well known. Above the 19^? level there are three weakly populated levels at 7402.1, 7849.2 and 8125.9 keV, which are likely to haveJ≥20. None of these energies agrees with the calculated value 7695±20 keV for the 20⁺ state of thei ₁₃ ^2/?4 configuration which has the highest angular momentum produced by the four valence neutron holes. This apparent anomaly can be understood if the yrast levels withJ≥20 have angular momentum contribution from the core. It seems likely that the states at 7402.1, 7849.2 and 8125.9 keV are due to proton core excited states of the typeπh _9/2 h ₁₁ ^2/?1 ×νp ₁ ^2/?2 i ₁₃ ^2/?2 withJ ^π=20⁺ andJ ^π=21⁺ andπh _9/2 h ₁₁ ^2/?1 ×νp ₁ ^2/?1 f ₅ ^2?1 i ₁₃ ^2/?2 withJ ^π=22⁺ or 23⁺, respectively. The state at 8126 keV has the highest energy so far directly observed in a stretched cascade ofγ-rays from the decay of a heavy nucleus produced in (α, xn) reactions.     

The Kepler-Coulomb problem on SO(2, 2) hyperboloid

In this note the Kepler-Coulomb problem in hyperbolic space H ₂ ² : z ₀ ² + z ₁ ² ? z ₂ ² ? z ₃ ² = R ² is discussed.     

Confrontation between the quasiparticle-phonon nuclear model and the interacting boson model for deformed nuclei

TheK ^π=0⁺, 2⁺ and 4⁺ states are considered in doubly even deformed nuclei. It is shown that in the quasiparticle-phonon nuclear model (QPNM) and in the interacting boson model (IBM) a vibrational state has one dominating component. The states withK _n ^π =0 ₃ ⁺ , 0 ₄ ⁺ 0 ₅ ⁺ 2 ₂ ⁺ , 2 ₃ ⁺ , 4 ₁ ⁺ and 4 ₂ ⁺ have a dominating one-phonon component within the QPNM and a two- or three-boson component within the IBM. According to the QPNM the contribution of two-phonon components to the wave functions of these states is less than 10%, i.e. there is a qualitative discrepancy in describing the structure of these states within the QPNM and the IBM. The experimental data indicate the existence in these states of one-phonon or two-quasiparticle components. They are rather well described within the QPNM. These states cannot be described within the IBM. This is due to the fact that the IBM takes into account only a small part of the space of two-quasiparticle states, just the one entering intoΒ- andγ-vibrational states.     

Probing the mesonic structure of the nucleon by means of exclusive quasielastic pion knockout in (e, e′π) reactions at high energies

By including the Z diagram in an analysis performed in the laboratory frame (instantaneous form of dynamics), the notion of quasielastic pion knockout by protons and electrons [(p, 2p) and (e, e′p) reactions treated in terms of the relevant pole diagrams] is generalized to the relativistic case where a meson is quasielastically knocked out of a nucleon by an electron having an energy of a few GeV. The concept of the wave function is introduced for the pion (and for other mesons), and its relation to the vertex constant G _πNN and the vertex function g _πNN(k ²) is indicated. The spectroscopic factor S _N ^B? is defined as the normalization of the wave function for the meson ?. It is shown by two methods that, under the kinematical conditions of quasielastic knockout that include the condition E _π?m _π (E _π is the energy of the knock-on pion) and the condition that the square Q ² of the virtual pion mass is large, the competing tree diagram is suppressed in relation to the pole diagram (this is not so in the case of pion photoproduction). From data of a p(e, e′π ⁺)n experiment involving longitudinal virtual photons γ _L ^* , the momentum distribution |Ψ _p ^nπ (k)|² of pions in the nucleon is extracted for the first time over the entire range of significant momenta k, and this result is used to determine the cutoff constant Λ_π and the value of S _p ^nπ ≈0.2. The momentum distribution of positive rho mesons in the soft section of the spectrum is determined from experimental data on the process p(e, e′π ⁺)n proceeding through the mechanism ρ ⁺+γ _T ^* → π ⁺ involving transverse photons. A way to determine the momentum distribution of omega mesons through data on the process p(e, e′π ⁰)p is indicated. Two forms of dynamics—instantaneous form and that of light-front dynamics (the latter does not involve the Z diagram)—are compared for the example where the calculations are performed for the spectroscopic factor S _N ^B? .     

Computable upper bounds for the adiabatic approximation errors

For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.     

Untersuchung des Zerfalls von134Cs durch γ-γ-Winkelkorrelationsmessungen

γ-γ-angular correlation measurements with Ge(Li) detectors and NaJ(Tl) detectors provided theE2/M1 mixing ratios of the following gamma transitions: 3 ₁ ⁺ →2 ₂ ⁺ (475.3 keV), 2 ₂ ⁺ →2 ₁ ⁺ (563.3 keV), 4 ₂ ⁺ →4 ₁ ⁺ (569.4 keV), 3 ₁ ⁺ →2 ₁ ⁺ (1,039 keV). The angular correlation measurements were only consistent with spin 3 of the 1,643 keV level. The half life of the 1,401 keV level was determined by delayed coincidence techniques to beT _1/2 (1,401 keV)≦30 ps.     

151,153Eu electron paramagnetic resonance in SrMoO4 and determination of signs of spin Hamiltonian parameters at different temperatures

The electron paramagnetic resonance (EPR) spectra of Eu²⁺ impurity centers in SrMoO₄ crystals have been studied in the temperature range of 1.8, 100–300 K. A hyperfine structure has been simulated for ^151,153Eu of different EPR transitions observed experimentally at different temperatures and external magnetic field orientations. A unique set of all parameters of the spin Hamiltonian for the known sign of the hyperfine interaction parameters A _i has been determined. It has been found that the diagonal parameters |b _n ⁰ | of the spin Hamiltonian decrease with increasing temperature; however, the parameter b ₄ ⁴ increases. The results of the study have demonstrated that |b ₂ ⁰ (T)/P ₂ ⁰ (T)| ～ const for ^151,153Eu in this single crystal.