Shell-model States Research Articles

Low- and high-spin excited states in 139Pr.

The level structure of the N=80 nucleus $^{139}\mathrm{Pr}$ has been studied in-beam by the $^{140}\mathrm{Ce}$(p,2n\ensuremath{\gamma}${)}^{139}$Pr reaction using a 25-MeV p beam and by the $^{139}\mathrm{La}$(\ensuremath{\alpha},4n\ensuremath{\gamma}${)}^{139}$Pr reaction using a 47-MeV \ensuremath{\alpha} beam. \ensuremath{\gamma}-ray singles, \ensuremath{\gamma}-\ensuremath{\gamma} coincidence (prompt and delayed), and \ensuremath{\gamma}-ray angular distribution experiments were performed. We have assigned 41 \ensuremath{\gamma} rays deexciting 24 states in $^{139}\mathrm{Pr}$ from the (p,2n\ensuremath{\gamma}) reaction and 43 \ensuremath{\gamma} rays deexciting 31 (generally higher-spin) states from the (\ensuremath{\alpha},4n\ensuremath{\gamma}) reaction, for a total of 43 different states. These in-beam experiments, taken together with results from $^{139}\mathrm{Nd}^{\mathrm{m}+\mathrm{g}}$ decay and the $^{141}\mathrm{Pr}$(p,t${)}^{139}$Pr reaction, allowed ${J}^{\ensuremath{\pi}}$ assignments to be made for most of the states and allowed us to deduce the intrinsic configurations for many of them. These are discussed in terms of single-quasiparticle shell-model states and triaxial weak-coupled collective states and are compared with systematics for this nuclear region.

Intruder states in odd-odd Tl nuclei: The completion of a unique set of intruder systematics

The α-decay of mass-separated Bi isotopes is studied to characterize shell-model intruder states in odd-odd Tl nuclei. By studying both experimentally and theoretically the members of the π 1 h 9 2 intruder-ν li 13 2 multiplet, the position of the intruder-based multiplet could be extracted. The scaling of intruder-state energies is discussed.

Quadrupole moments of the [formula omitted] and 7 + isomers in 117, 118Sb and the deformation induced by the [formula omitted] proton-hole intruder state

The electric quadrupole moments of the 117Sb(23/2 −) and 118Sb(7 +) isomers involving in their structure the 1 g 9 2 −1 proton-hole shell-model intruder state have been measured by the TDPAD method. From the obtained results, |Q| ( 23 2 −)=246(25) fm 2 and | Q|(7 +)=175(30) fm 2, large deformations of 0.24(3) and 0.20(4), respectively, have been deduced for the two high-spin isometric states in 117, 118Sb.

Configuration mixing and electromagnetic properties of odd-even nuclei.

The electromagnetic properties of ground and excited states of nuclei with an odd number of particles and holes outside the closed shells are described in the j-j coupling shell model. The residual interaction between the valence particles and holes causes two different configuration mixing: (a) one where the valence particles and holes are scattered to higher shell model states, and (b) ones where the valence particles and holes excite particles out of the core. The electromagnetic properties of odd-even nuclei are sensitive to the correct treatment of both types of configuration mixing. In this paper the matrix elements of the nuclear Hamiltonian evaluated using the basis of configuration mixing states of types (a) and (b), and the resulting eigenvalue equations, have been exactly calculated. The matrix elements of the electromagnetic multipole operators calculated with the resulting eigenvectors of type (b) are then related to the deviation observed between the experimental and valence expectation values.

Analytic solution of the covariant shell model of three dirac fermions with harmonic forces

A covariant shell model of three Dirac fermions in the center-of-mass frame is analytically solved for a particular spin-dependent harmonic-oscillator potential. Three equal-mass quarks are all assumed to be in states with identical quantum numbers ofjπ=1/2+ for the shell-model ground state. The sixtyfour-component composite wave function for three Dirac fermions is reduced to a set of four coupled differential equations for the four independent composite radial components. Hyperspherical coordinates are used. The two-body potential used vanish in the small component of the composite wave function. The various components of the composite wave function are found to have aρl exp(−κρ2) hyperradial dependence, where ρ is the hyperradius, andl is the sum of the orbital angular momentum acting in the various components of the composite wave function. For an eigenergy equal to the proteon rest-mass energy, the root-mean-square radius calculated is about 0.84 fermi, about 80% of that calculated in an independent-particle harmonic-oscillator model with the same rest-mass energy for the system. A sixth-order polynomial equation is found for the rest-mass energy of the system in terms of the potential-strength parameter, and the quark mass, For a quark mass of zero, a quadratic equation inE3 is obtained. One solution agrees with earlier work, and the other can be rejected on physical grounds. The various components of the composite three-body wave function are dominated by thel=0s-state component as the quark mass approaches one third of the system rest-mass energy. For zero quark mass thes-wave component is about 29% of the normalization, thep wave about 44%, thed wave about 22%, and thef wave 4% of the normalization.

A study of some (sd)4 shell model states in20F via the18O(3He, p) reaction

A microscopic two-particle DWBA analysis is carried out on the18O(3He, p)20F reaction leading to the (sd)4 positive-parity levels. The spectroscopic amplitudes were derived from the three single-particle energies and sixty-three two-body matrix elements given by the shell model calculations or Halbertet al. based on an inert16O core with the additional nucleons distributed in an unrestricted 1d5/2-2s1/2-1d3/2 model space. Angular distributions leading to several 1+, 2+, 3+, 4+ and 5+ (sd)4 levels in20F are fairly well reproduced.

Codes for the combinatorial calculation of few quasiparticle state densities in spherical and deformed nuclei

The codes for combinatorial calculation of few quasiparticle state and level densities are presented. The calculations are performed in the space of the shell-model single particle states and include pairing interaction explicitly. The spin and parity distributions of quasiparticle states are also provided. The calculations can be restricted to the states with all quasiparticles being bound.

In-beam investigations and structure studies of multiparticle excitations in the N = 82, 83 nuclei 138,139Ba

Abstract Excited states of 138Ba populated via the 136Xe(gas)(α, 2n) reaction have been studied by in-beam measurements of γγ-coincidences, excitation functions, angular distributions and the linear polarization of the γ-radiation as well as the γ-ray time distributions relative to the beam pulses and the Doppler shift of the γ-ray energy. The level scheme of 138138Ba could be extended by 10 new levels with spin values up to 12ħ and excitation energies up to 4864 keV. For the 71+, 81+, 101+ and 91− levels subnanosecond lifetimes have been determined, while for 5 further states upper limits of their lifetimes could be derived. Additionally, 4 new levels of 139Ba have been established which were populated via the (α, n) reaction channel. Among them the level at Ex = 1977 keV was found to be isomeric. The experimental data on excitation energies and electromagnetic properties of even-parity 138Ba levels are compared with predictions of the spherical shell model. Odd-parity states of 138Ba and 139Ba are interpreted in terms of a particle-core coupling approach which describes the coupling of one 1 h 11 2 proton and one 2 f 7 2 neutron, respectively, to π = + 1 shell-model states of the corresponding (A − 1) core nuclei. A rather good agreement between experiment and theory can be stated.

Doorway states induced by quantum recoils.

A proper treatment of the Pauli principle is usually impossible in Jacobi coordinate representation when heavy nuclei are involved; hence a shell-model representation of the collision becomes mandatory. This raises the traditional problems of shell-model spurious states and recoil corrections. We show how recoil parameters can actually be used as dynamical parameters in collision theories.

Number projection method.

A relationship between the number projection and the shell model methods is investigated in the case of a single-j shell. We can find a one-to-one correspondence between the number projected and the shell model states.

Electroweak Bosons, Leptons and Han-Nambu Quarks in a Unified Spinor-Isospinor Preon Field Model

The model is defined by a selfregularizing nonlinear spinor-isospinor preon field equation and all observable (elementary and non-elementary) particles are assumed to be bound states o f the quantized preon field. In a series o f preceding papers this model was extensively studied. In particular for com posite electroweak bosons the Yang-Mills dynamics was derived as the effective dynamics o f these bosons. In this paper the first generation o f com posite leptons and com posite Han-Nam bu quarks is introduced and together with electroweak bosons, these particles are interpreted as “shell model” states o f the underlying preon field. The choice o f the shell model states is justified by deriving the effective fermion-boson coupling and demonstrating its equivalence with the phenom enological electroweak coupling terms o f the Weinberg-Salam model. The investigation is restricted to the left-handed parts o f the composite fermions. Color is revealed to be a hidden orbital angular momentum in the shell model and hypercharge follows from the effective coupling. The techniques o f deriving effective interactions is a “weak mapping” procedure and the calculations are done in the “low” energy limit.

Transfer reactions for 28Si

Cross sections of one- and few-nucleon transfers in the reaction /sup 28/Si+ /sup 28/Si at E/sub lab/ -- 151.25 MeV have been measured with a quadrupole-dipole-dipole-dipole magnetic spectrometer. The one-neutron and one-proton transfers to corresponding shell model states in the pairs of mirror nuclei /sup 29/Si-/sup 29/P and /sup 27/Si-/sup 27/Al are found to be approximately equal. The cross sections for few-nucleon transfers to states with excitation energies E/sub x/<5 MeV exhibit a strong enhancement of 1n1p over 2n and 2p and of 2n2p (i.e., 1..cap alpha..) over 2n1p or 1n2p transfers. A distorted-wave Born approximation analysis of the 1n and 1p transfers was performed. The derived spectroscopic factors display a high degree of symmetry with respect to isospin and are consistent with the widely varying values obtained in light ion studies.

Construction of microscopic boson states and their relevance for IBM-2

We investigate four methods for the construction of collective shell model states which may be mapped onto boson states of the IBM-2. These methods use, as building blocks for the wave functions, particle-particle pair operators, particle-hole operators, pair operators with seniority projection and energy-weighted quadrupole operators. It is demonstrated that one obtains stronger collectivity with the energy-weighted quadrupole operator than with the other methods. On the basis of a comparison of calculated and empirical IBM-2 interaction parameters we can rule out the seniority projection method. This implies that particle-particle and particle-hole approaches difler. The ratios between quadrupole matrix elements of the microscopic boson states appear to be similar to the IBM predictions. For states corresponding to those with two d-bosons coupled to J = 0 there is a smaller quadrupole matrix element when subshells with small angular momenta dominate near the Fermi level. Especially for this type of states the collective quadrupole space will be larger than represented in the IBM, however, which may compensate the smaller proton-neutron quadrupole coupling. The calculated bare quadrupole interaction between like bosons is found to be weak.

Electromagnetic properties through two band crossings in 165Lu

The two signatures of a band built on a π h 11 2 shell model state have been established to high spin (I π = 65 2 − ) in 165Lu. An observed second band crossing at ℏ ω ∼ 0.40 MeV is interpreted as the alignment of a second pair of i 13 2 neutrons. M1 transitions are observed through both crossing and the data utilized in connection with the observed signature splitting of energies and alignments to interpret the measured values of B( M1, I → I − 1) Q 2 0 . Alignment effects and shape changes are discussed.

Study on the 208Pb(α, 6He) 206Pb reaction at Eα = 109 MeV

The 208Pb(α, 6He) 206Pb reaction induced by 109 MeV α particles has been studied with 70 keV energy resolution. Twenty-five transitions up to 6.2 MeV in excitation energy have been analyzed. The shapes of the angular distributions are reproduced well by the zero-range distorted-wave Born approximation (DWBA) calculations. The spin and parity of the level at 6.10 MeV are proposed to be 9 −. It is interpreted as a weakly-coupled state of the collective 3 − state and the two-hole 6 + shell-model state. The energy dependence of the total cross sections of the (α, 6He) and (p, t) reactions has been studied systematically by using our present data and other data from the literatures. It reveals that there exists an empirical rule which allows one to compare quantitatively the ratios of the transition strengths of both reactions. The transition strength of the (α, 6He) reaction is found to be about 35 times smaller than that of the (p, t) reaction for the transitions to the natural parity states, while it is about 15 times smaller for the transition to the unnatural parity 3 + state. These small transition strengths are explained by the fact that this reaction occurs at the surface region of the nucleus.

Shell-model interaction energies in a relativistic hamiltonian formulation (I)

The non-covariant hamiltonian formulation of relativistic field theory is presented and solved as a secular problem in a discrete representation space. The shell-model two-nucleon interaction in the one-boson exchange picture is used to test the method before applying it to many-body systems. The results of the diagonalization treatment are convergent as a function of the discretized meson space and are close to the usual OBEP when considering the exchange of a single type of meson, thus establishing the numerical feasibility of the method. However a significant deviation between the two approaches appears for the sigma meson or for a mixture of several types of mesons with values of the coupling constants in the “physical” domain. Also, in the limited momentum space of the nucleons in the lowest shell-model state, the cut-off in the nucleon vertex form factors plays an unimportant role.

In-beam gamma -ray spectroscopy of excited states in 141Pm.

The level structure of the N = 80 nucleus /sup 141/Pm has been studied in-beam by the /sup 142/Nd(p,2n..gamma..)/sup 141/Pm reaction using a 25-MeV p beam and by the /sup 141/Pr(..cap alpha..,4n..gamma..)/sup 141/Pm reaction using a 47-MeV ..cap alpha.. beam. ..gamma..-ray singles, ..gamma..-..gamma.. coincidence (both prompt and delayed), and angular distribution experiments were performed. We found 42 ..gamma.. rays deexciting 28 states in /sup 141/Pm from the (p,2n..gamma..) reaction and 34 ..gamma.. rays deexciting 22 (generally higher-spin) states from the (..cap alpha..,4n..gamma..) reaction, for a total of 35 known states in /sup 141/Pm. These in-beam experiments, taken together with the results from /sup 141/Sm/sup m/+g decay, yield J/sup ..pi../ assignments for most of the states and have allowed us to deduce the configurations for many of the states. The structures are discussed in terms of single-quasiparticle shell-model and triaxial weak-coupled collective states and are compared with systematics for this nuclear region.

On the geometrical shape of the single particle spin-orbit potential

A good description of the single particle shell model states near the Fermi surface, after including core polarization correction, can be obtained by taking identical geometrical shapes for both central and spin orbit potential thus reducing the number of free parameters in the scattering analysis. This bary centric approach also reproduces the charge distribution admirably.

Core polarisation effect on the 3p 1/2, 3p 3/2, 2f 5/2, 2f 7/2 and 1i 13/2 proton states of209Bi

The weak fragments of the 3p1/2, 3p3/2, 2f5/2, 2f7/2 and 1i13/2 proton states of209Bi as seen in the208Pb (3He,d) reaction can be explained with the coupling of the renormalised proton states and the vibrational states of208Pb. The energies of the zerothorder proton shell-model states as well as the collective admixtures of the weak fragmented proton states of209Bi have been deduced from the core-particle coupling model.

A shell-model interpretation of intruder states and the onset of deformation in even-even nuclei

By simple consideration of the relative magnitude of the proton-neutron interaction (especially the monopole and quadrupole components) and the energy gaps between spherical shell-model states near shell and subshell closures, a shell-model interpretation of both the occurrence of low-lying intruder states in certain mass regions and of the onset of stable deformation in the ground state in others, is obtained. It is shown that in the Cd region near A ≅ 114, spherical ground states with low-lying intruder 0 + configurations result whereas deformation should occur in the A ≅ 100 ( Z = 40) and the A ≅ 150 ( Z = 64) mass regions.