Finite Abnormal Nuclei

We solved the problem for both the normal and abnormal finite nuclei from a simple relativistic model,and found eritical mass numbers A₁=85 and A₂=165.Only nuclei with mass numbers A≥A₁ may bave bound abnormal states,and only abnormal nuclei with mass number A≥A₂ have binding energies larger than those of corresponding normal nuclei.Abnormal nuclei become unbound again if A>3310,because of the Coulomb repulsion.     

Beta-decay energies of neutron-rich nuclei in the mass region 142≦A≦150

The β-endpoint energies of 6 neutron-rich nuclei with mass numbersA=146 andA=147 have been measured with a plastic scintillator telescope at the on-line mass separator OSTIS. With theQ _β-values derived from these experiments and with those obtained in earlier studies, nuclear structure effects in this part of the nuclear chart are investigated. In addition, nuclear masses derived from the experimentalQ _β-values are compared with the predictions of theoretical mass calculations.     

Experimental Beta-decay energies of very neutron-rich fission products with 107≦A≦109

Theβ-decay of neutron-rich fission products with mass numbersA=107, 108 and 109 has been investigated at the mass separator LOHENGRIN of the Institute Laue-Lange-vin (ILL) in Grenoble by measuringβγ-coincidences with a large plastic scintillator telescope and a Ge(I)-detector. Theβ-decay energies of 8 nuclei were obtained from the evaluation of more than 40β-endpoint energies. For the nuclei¹⁰⁷ Mo,¹⁰⁷Tc,¹⁰⁸Tc,¹⁰⁹Tc and¹⁰⁹Ru, theβ-decay energies were determined for the first time; the experimental error in the decay energy of three daughter nuclei was considerably reduced. In addition, the two-neutron separation energies and the nuclear mass excesses were calculated from these experimentalQ _β-values and compared with different mass predictions.     

Experimental study on the 3p size-resonance in thep- wave neutron strength function

Using a silicon filtered fission neutron beam of an energy width of 20 keV around 143 keV we measured the total cross sections for 37 nuclides and elements having mass numbers between 87 and 140 and determined thep-wave strength functions. The 3P-resonance atA=98 shows no splitting into theP _3/2?P _1/2 doublet. The narrow resonance peak and the following broad distribution of thep-strength function (A=103 to 140) can approximately be reproduced by deformed optical model calculations. The spin-orbit term in the optical potential is consistent with the spin orbit force in the shell model. For nuclei around the closed (N=50) neutron shell a shell effect in thep-wave strength function is indicated.     

The calculation of logft values and spectroscopic factors for nuclei in the mass range 10–15

Wave functions obtained in previous shell-model calculations [1, 2] for states of nuclei with massesA=10–15 are used to calculate logft values and spectroscopic factors. These wave functions, which were based on a modified surface delta two-body interaction, comprise the following active shell-model spaces: the 1p _3/2 and 1p _1/2 orbitals for mass 10–14 nuclei and restricted combinations of the 1p _1/2, 2s _1/2, 1d _5/2 and 1d _3/2 orbitals for mass 15 nuclei, leading to four different calculations in the latter case. The calculated results support evidence that the modified surface delta interaction is a valid approximation to the effective interaction in light nuclei.     

Investigation of (n, 2n) reactions by the evaporation process

The (n, 2n) cross sections for about 80 nuclei ranging fromA=45 to 209 were calculated using the evaporation model. The calculation was performed for incident energiesE _n which satisfy the conditionU _R =E _n +Q _n ,2n=6±1 MeV. For 11 nuclei in the above mass region, (n, 2n) excitation functions were calculated from threshold to 20 MeV. In all calculations a single set of input parameters was consistently used. The influence of the level-density parameter and neutron cross sections on the evaporation model was tested. All calculated results were compared with experimental data. The systematic discrepancy between experimental data and evaporation calculations leads to the necessity of introducing the preequilibrium emission mechanism.     

Coexistence of terminating bands and more collective bands in theA ∼ 100 region of nuclei

Nilsson-Strutinsky cranking calculations onA≥100 Ru and Pd nuclei suggest that, contrary to other mass regions, it should be possible to follow the ground state rotational bands to their termination at spins just aboveI=30? and then also to observe other bands which terminate at higher spins.     

Heavy fragments produced in proton-nucleus and nucleus-nucleus collisions at relativistic energies

Mesons, nucleons and light and heavy nuclei are observed as a result of a proton-nucleus or a nucleus-nucleus collision at relativistic energies (E_p≥0.5 GeV/u). This review concentrates on the properties of the heavy fragment nuclei (A ≥10. The experimental results for the distributions in mass, charge, angle and kinetic energy are presented. The data are discussed in the framework of models for spallation, fission and multifragmentation.     

Hölder’s inequality for matrices

We prove that for arbitraryn×n matricesA ₁,A ₂,…,A _m and for positive real numbersp ₁,p ₂,…,p _m withp ₁ ^?1 +p ₂ ^?1 +…+p _m ^/?1 =1, the inequality 1 $$|Tr(A_1 A_2 ...A_m )^2 |< \mathop {II}\limits_{k = 1}^m [Tr(A_k^\dag A_k )^{p_k } ]P_k^{ - 1} $$ holds.     

Energetics of the fission process

The mass asymmetry of fragments from nuclear fission of heavy nuclei is reviewed. While mass asymmetry is a common and well-known phenomenon for low-energy fission of the lighter actinides, more recent experiments have demonstrated that, for the heaviest actinides, the mass distribution switches to a symmetric one. On the other hand, it has been discovered that, though for fissioning nuclei with mass numbersA225 the mass distribution is basically symmetric, an asymmetric component is clearly to be identified for nuclei down to the Pb-region. In the absence of a generally accepted dynamical theory of fission, the above experimental findings are discussed in terms of static energy considerations. Triggered from the outset by the structure of the potential energy surface at the saddlepoint, the energy balance at the scission point between the available energy (Q-value) of the reaction and the Coulomb and deformation energy of the nascent fragments is shown to steer the characteristics of the fragment mass distributions.     

Die Coulomb-Energien leichter Atomkerne

A compilation of the known data on Coulomb energy differences of isobaric doublets and isobaric triplets is given. Plots of the Coulomb energy differences versus¯Z/A ^1/3 with¯Z=(Z ₁+Z ₂)/2 show an analogous shell structure behaviour for the three series with 2¯Z=A?1,A andA+1 (T=1, 1/2 and 1), i.e. discontinuities at the closed shells atA=4, 16 and 40 and the closed subshell atA=32 and oscillations mainly being due to Coulomb proton-proton pairing energy. A positive energy shift of the lowest states withT=1 of all self-conjugate nuclei withA=4n+2 seems to be indicated by the experimental data. A semi-empirical formula is given that describes the data.     

Fragmentation of gold projectiles: From evaporation to total disassembly

We have studied the fragmentation of Au projectiles interacting with targets of C, Al and Cu at an incident energy ofE/A=600 MeV. The employed inverse kinematics allowed a nearly complete detection of projectile fragments with chargeZ≧2. The recorded fragmentation events were sorted according to three observables, the multiplicityM _lp of light charged particles, the largest atomic numberZ _max within an event, and a new observable,Z _bound, representing the sum of the atomic numbersZ of all fragments withZ≧2. Using these observables, the impact parameter dependence of the fragmentation process was investigated. For all three targets, a maximum mean multiplicity of 3 to 4 intermediate mass fragments (IMFs) is observed. The corresponding impact parameters range from central collisions for theC target to increasingly peripheral collisions for the heavier targets. It is found that the correlation between the IMF multiplicity andZ _bound, extending from evaporation type processes (largeZ _bound) to the total disassembly of the projectile (smallZ _bound), is independent of the target nucleus. This universal behaviour may suggest an — at least partial — equilibration of the projectile fragment prior to its decay.     

Binding energies and radii of α-cluster-type nuclei from calculations based on the strictly restricted dynamics model

The properties of α-cluster-type nuclei with 4≤A≤80 are studied by employing the microscopic strictly restricted dynamics model (SRDM). The SRDM parameter set found via a fit to the experimental and theoretical values of nuclear binding and excited-level energies, classified according to the ground-state SU ₃ configurations, includes a nuclear-radius parameter r ₀ entering into the expression R=r ₀ A ^1/3 [fm], as well as the parameters of the effective central NN-interaction potential. The use of the microscopic SRDM allows one to obtain additional information about nuclei along the Z=N line, including binding energies, radii, and spectra of low-lying levels. The calculated nuclear binding energies and nuclear root-mean-square radii 〈r ²〉^1/2 are in reasonable agreement with their experimental counterparts.     

The role of isospin on the N=Z line

The role played by isospin in nuclear structure phenomena encountered on the N=Z line is discussed. New results on Coulomb energy differences (CED) at high spin for odd-A nuclei in the f _7/2 shell are presented and interpreted in the framework of a simple Cranked Shell Model treatment involving an exact numerical diagonalisation. Results for the CED between the A=46 even-even mirror pairs are also discussed. The CED between the T=1 states in N=Z odd-odd nuclei and their isobaric analogues are suggested as a possible probe of np pairing on the N=Z line. First results from a numerical diagonalization of IBM-4 are cited.     

Theory of chemical equilibrium in a lattice

The chemical equilibrium is studied for the reactionA+B?C, assuming that, initially, the particlesB form a lattice and the particlesA are statistically distributed on interstices. A mass action law is derived which defines the numbersn _A, n_B, n_C of particlesA, B,C in the chemical equilibrium assuming the initial distribution to be known. It predicts a considerably larger numbern _C of fused particlesC compared to the mass action law for the gaseous phase. The result holds for an ordinary as well as for a nuclear lattice. Its possible relevance for the production of proton-rich isotopes in the universe is discussed.     

New neutron magic number <Emphasis Type="Italic">N</Emphasis> = 16 for neutron-rich nuclei

A survey of experimental results obtained at GANIL (Caen, France) on the study of the properties of very neutron-rich nuclei (Z=6–20, A=20–60) near the neutron drip line and resulting in an appearance of further evidence for the new magic number N=16 is presented. Very recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells, and together with the measurements of instability of doubly magic nuclei ¹⁰He and ²⁸O, they provide information on changes in neutron shell closures of very neutron-rich isotopes. The behavior of the two-neutron separation energies S_2n derived from mass measurements gives very clear evidence for the existence of the new shell closure N=16 for Z=9 and 10 appearing between the 2s_1/2 and 1d_3/2 orbitals. This fact, strongly supported by the instability of C, N, and O isotopes with N>16, confirms the magic character of N=16 for the region from carbon up to neon, while the shell closure at N=20 tends to disappear for Z≤13. Decay studies of these hardly accessible short-lived neutron-rich nuclei from oxygen to silicon using in-beam γ-ray spectroscopy are also reported.     

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.     

Q1(1290) and Q2 (1400) decay rates and their SU(3) implications

We summarize and combine the known information on the decay rates of the strangeness-one axial vector mesons, Q₁ and Q₂. From this information and the rate for B→ωπ, we determine the Q_A?Q_B mixing angle and the S-wave, symmetric and antisymmetric octet couplings for vector-pseudoscalar decays of axial vector mesons. If we assume the D(1285) and the E(1420) belong to the J^PC=1⁺⁺ nonet, we find the A₁ to have a mass of ～1.47 GeV and a large (>0.3 GeV) width.     

New isomers and their decay in odd-odd neutron-deficient cesium isotopes

By a systematic on-line cesium mass separation fromA=122 toA=132 and subsequent gamma and electron decay spectroscopy at very low energy, new isomers have been precisely identified:^122m Cs (T _1/2=0.36±0.02 s),^124m Cs (T _1/2=6.3±0.2 s) and^130m Cs (T _1/2=3.46±0.06 min). Detailed level schemes are given for both^124m Cs and^130m Cs. Comparison of excited levels known in the odd-odd nuclei of the same region shows that more experimental informations are needed to propose a clear and realistic picture of the nuclear states structure. Radioactivity:^{122m, 124m, 130m} Cs [from La or Ce,³Hexn]-measuredT _1/2,E _γ,I _γ,E _CE ,I _CE ,γ-γ-t, γ-ce coinc.; deduced ICC,^{124, 130}Cs deduced levels,J, π. Online mass separated sources, Ge(Li), intrinsic Ge, Si(Li), magnetic electron selector.     

The moment of inertia at the saddle point of low energy fission of even-even nuclei

We use the molecular model of low energy fission, which describes the nucleus by two interacting fragments, to calculate the moment of inertia for U²³⁶ in the cranking approximation including BCS theory. We show that the moment of inertia at the saddle point:

1. depends almost linearly on the fragment distance.
2. is influenced only very weakly by the pairing constant and by the fragment deformations.
3. shows, as a function of the distribution of mass between the two fragments (A ₁ ,A ₂ ), a minimum near the magic configurationA ₁=132,Z ₁=50 and depends in this mass region strongly on the term structure near the Fermi energy.
4. is approximately that of a rigid body.