A new 7 mus isomer in the drip line nucleus 140Dy was selected from the products of the 54Fe (315... more A new 7 mus isomer in the drip line nucleus 140Dy was selected from the products of the 54Fe (315 MeV) + 92Mo reaction by a recoil mass spectrometer and studied with recoil - delayed gamma-gamma coincidences. Five cascading gamma transitions were interpreted as the decay of an Ipi = 8- {v9/2-[514] ⊗ v7/2+[404]} K isomer via the ground state
Background: In coupled-channel models the poles of the scattering S-matrix are located on differe... more Background: In coupled-channel models the poles of the scattering S-matrix are located on different Riemann sheets. Physical observables are affected mainly by poles closest to the physical region but sometimes shadow poles have considerable effect, too.
The real Scarf II potential is discussed as a radial problem. This potential has been studied ext... more The real Scarf II potential is discussed as a radial problem. This potential has been studied extensively as a one-dimensional problem, and now these results are used to construct its bound and resonance solutions for l = 0 by setting the origin at some arbitrary value of the coordinate. The solutions with appropriate boundary conditions are composed as the linear combination of the two independent solutions of the Schrödinger equation. The asymptotic expression of these solutions is used to construct the S 0 (k) s-wave S-matrix, the poles of which supply the k values corresponding to the bound, resonance and anti-bound solutions. The location of the discrete energy eigenvalues is analyzed, and the relation of the solutions of the radial and one-dimensional Scarf II potentials is discussed. Analogies with the generalized Woods-Saxon and the Rosen-Morse II potential are pointed out.
Two observations of fine structure in proton emission are reported : 3-µs 145 Tm and 4-ms 141 Ho.... more Two observations of fine structure in proton emission are reported : 3-µs 145 Tm and 4-ms 141 Ho. These experiments were performed using the Recoil Mass Separator (RMS) at the Holifield Radioactive Ion Beam Facility at Oak Ridge. The signals from the RMS detectors were digitally processed using Digital Gamma Finder modules. The fine structure branching ratios, 9.6 ¡
In a cut-off Woods-Saxon potential with realistic depth S-matrix poles being far from the imagina... more In a cut-off Woods-Saxon potential with realistic depth S-matrix poles being far from the imaginary wave number axis form a sequence where the distances of the consecutive resonances are inversely proportional with the cut-off radius value. Other poles lying closer to the imaginary wave number axis might have trajectories with irregular shapes as the depth of the potential increases.
Acta Physica Academiae Scientiarum Hungaricae, 1981
Exact finite range DWBA calculation performed for the reaction12C(6Li, d)16O* [6.05] reproduces s... more Exact finite range DWBA calculation performed for the reaction12C(6Li, d)16O* [6.05] reproduces satisfactorily the 18 MeV experimental cross section and yields a value of 0.17 for the product of the spectroscopic factors. A comparison of the results with two approximate descriptions shows that the finite range effects induce more oscillations in the angular distribution and depress the maxima at medium and backward angles. A finite range correction calculation with 1.5 fm for the finite range parameter is acceptable for describing the experimental data.
By adjusting the parameters of the new phenomenological nuclear potential introduced recently by ... more By adjusting the parameters of the new phenomenological nuclear potential introduced recently by P. Salamon and T. Vertse (2008) (SV) to the global potential sets of Perey and of Becchetti and Greenlees, it is shown that the SV potential well approximates the cut-off Woods--Saxon (CWS) form even if its second term is set to zero. The important difference between the CWS and SV potentials is that CWS jumps to zero at the cut-off radius, while the SV potential goes to zero smoothly. We fitted the single-term SV potential to the global potentials, and compared the spectra and the pole trajectories of neutron single-particle states generated by some light neutron-deficient nuclei that are most often used in positron emission tomography (PET): $^{13}$N, $^{15}$O and $^{18}$F. The CWS and the SV energies agree reasonably well, and only the pole trajectories, which span extremities, are substantially different.
An unified shell model scheme to evaluate simultaneously the contributions of bound singleparticl... more An unified shell model scheme to evaluate simultaneously the contributions of bound singleparticle states, Gamow resonances, antibound (virtual) states and continuum complex scattering states is presented. The formalism could be very suitable to study processes occurring in the continuum part of the nuclear spectra El espectro continuo de un sistema de muchos cuerpos presenta ciertas propiedades características de sistemas resonantes, como por ejemplo secciones eficaces con picos muy definidos a energías cercanas a la resonacia, o un cambio rápido en el desfasaje ("phase shift") a la energía de resonancia. Este estado resonante puede ser descripto, para resonancias angostas, aproximadamente por un vector de Gamow, esto es, un autovector generalizado del Hamiltoniano del sistema con energía compleja. Estas energías son polos de la extensión analítica de la matris S, como también lo son las energías correspodientes a los estados ligados. Además de estos polos la matris S tiene otros polos sobre el eje imaginario negativo. Los estados asociados con estos polos se los llama estados anti-ligados o estados virtuales. Cuando el polo está muy cerca del eje real produce efectos observables en la sección eficaz. En este trabajo mostramos como incluir tales estados en el modelo de capas y lo aplicamos a un sistema nuclear donde es conocido que tal efecto existe.
New isomeric states were identified in the dripline nucleus ^140Dy with a half-life of 7 mus[1,2]... more New isomeric states were identified in the dripline nucleus ^140Dy with a half-life of 7 mus[1,2] and in ^140Eu (t_1/2 = 300 ns) in an experiment at the focal plane of the RMS at HRIBF. The isomers were produced by bombardment of a 1 mg/cm^2 target of ^92Mo with 315 MeV ^54Fe. Level schemes have been constructed based on gamma-gamma
The parameters of the nuclear liquid drop model, such as the volume, surface, symmetry, and curva... more The parameters of the nuclear liquid drop model, such as the volume, surface, symmetry, and curvature constants, as well as bulk radii, are extracted from the non-relativistic and relativistic energy density functionals used in microscopic calculations for finite nuclei. The microscopic liquid drop energy, obtained self-consistently for a large sample of finite, spherical nuclei, has been expanded in terms of powers of A −1/3 (or inverse nuclear radius) and the isospin excess (or neutron-to-proton asymmetry). In order to perform a reliable extrapolation in the inverse radius, the calculations have been carried out for nuclei with huge numbers of nucleons, of the order of 10 6 . The Coulomb interaction has been ignored to be able to approach nuclei of arbitrary sizes and to avoid radial instabilities characteristic of systems with very large atomic numbers. The main contribution to the fluctuating part of the binding energy has been removed using the Green's function method to calculate the shell correction. The limitations of applying the leptodermous expansion to actual nuclei are discussed. While the leading terms in the macroscopic energy expansion can be extracted very precisely, the higher-order, isospin-dependent terms are prone to large uncertainties due to finite-size effects.
Shell corrections to the nuclear binding energy as a measure of shell effects in superheavy nucle... more Shell corrections to the nuclear binding energy as a measure of shell effects in superheavy nuclei are studied within the self-consistent Skyrme-Hartree-Fock and Relativistic Mean-Field theories. Due to the presence of low-lying proton continuum resulting in a free particle gas, special attention is paid to the treatment of single-particle level density. To cure the pathological behavior of shell correction around the particle threshold, the method based on the Green's function approach has been adopted. It is demonstrated that for the vast majority of Skyrme interactions commonly employed in nuclear structure calculations, the strongest shell stabilization appears for Z=124, and 126, and for N =184. On the other hand, in the relativistic approaches the strongest spherical shell effect appears systematically for Z=120 and N =172. This difference has probably its roots in the spin-orbit potential. We have also shown that, in contrast to shell corrections which are fairly independent on the force, macroscopic energies extracted from self-consistent calculations strongly depend on the actual force parametrisation used. That is, the A and Z dependence of mass surface when extrapolating to unknown superheavy nuclei is prone to significant theoretical uncertainties.
Shell corrections of the finite deformed Woods-Saxon potential are calculated using the Green's f... more Shell corrections of the finite deformed Woods-Saxon potential are calculated using the Green's function method and the generalized Strutinsky smoothing procedure. They are compared with the results of the standard prescription which are affected by the spurious contribution from the unphysical particle gas. In the new method, the shell correction approaches the exact limit provided that the dimension of the single-particle (harmonic oscillator) basis is sufficiently large. For spherical potentials, the present method is faster than the exact one in which the contribution from the particle continuum states is explicitly calculated. For deformed potentials, the Green's function method offers a practical and reliable way of calculating shell corrections for weakly bound nuclei.
Two methods the complex energy shell model (CXSM) and the complex scaling (CS) approach were used... more Two methods the complex energy shell model (CXSM) and the complex scaling (CS) approach were used for calculating isobaric analog resonances (IAR) in the Lane model. The IAR parameters calculated by the CXSM and the CS methods were checked against the parameters extracted from the direct numerical solution of the coupled channel Lane equations (CC). The agreement with the CC results was generally better than 1 keV for both methods and for each partial waves concerned.
A new 7 mus isomer in the drip line nucleus 140Dy was selected from the products of the 54Fe (315... more A new 7 mus isomer in the drip line nucleus 140Dy was selected from the products of the 54Fe (315 MeV) + 92Mo reaction by a recoil mass spectrometer and studied with recoil - delayed gamma-gamma coincidences. Five cascading gamma transitions were interpreted as the decay of an Ipi = 8- {v9/2-[514] ⊗ v7/2+[404]} K isomer via the ground state
Background: In coupled-channel models the poles of the scattering S-matrix are located on differe... more Background: In coupled-channel models the poles of the scattering S-matrix are located on different Riemann sheets. Physical observables are affected mainly by poles closest to the physical region but sometimes shadow poles have considerable effect, too.
The real Scarf II potential is discussed as a radial problem. This potential has been studied ext... more The real Scarf II potential is discussed as a radial problem. This potential has been studied extensively as a one-dimensional problem, and now these results are used to construct its bound and resonance solutions for l = 0 by setting the origin at some arbitrary value of the coordinate. The solutions with appropriate boundary conditions are composed as the linear combination of the two independent solutions of the Schrödinger equation. The asymptotic expression of these solutions is used to construct the S 0 (k) s-wave S-matrix, the poles of which supply the k values corresponding to the bound, resonance and anti-bound solutions. The location of the discrete energy eigenvalues is analyzed, and the relation of the solutions of the radial and one-dimensional Scarf II potentials is discussed. Analogies with the generalized Woods-Saxon and the Rosen-Morse II potential are pointed out.
Two observations of fine structure in proton emission are reported : 3-µs 145 Tm and 4-ms 141 Ho.... more Two observations of fine structure in proton emission are reported : 3-µs 145 Tm and 4-ms 141 Ho. These experiments were performed using the Recoil Mass Separator (RMS) at the Holifield Radioactive Ion Beam Facility at Oak Ridge. The signals from the RMS detectors were digitally processed using Digital Gamma Finder modules. The fine structure branching ratios, 9.6 ¡
In a cut-off Woods-Saxon potential with realistic depth S-matrix poles being far from the imagina... more In a cut-off Woods-Saxon potential with realistic depth S-matrix poles being far from the imaginary wave number axis form a sequence where the distances of the consecutive resonances are inversely proportional with the cut-off radius value. Other poles lying closer to the imaginary wave number axis might have trajectories with irregular shapes as the depth of the potential increases.
Acta Physica Academiae Scientiarum Hungaricae, 1981
Exact finite range DWBA calculation performed for the reaction12C(6Li, d)16O* [6.05] reproduces s... more Exact finite range DWBA calculation performed for the reaction12C(6Li, d)16O* [6.05] reproduces satisfactorily the 18 MeV experimental cross section and yields a value of 0.17 for the product of the spectroscopic factors. A comparison of the results with two approximate descriptions shows that the finite range effects induce more oscillations in the angular distribution and depress the maxima at medium and backward angles. A finite range correction calculation with 1.5 fm for the finite range parameter is acceptable for describing the experimental data.
By adjusting the parameters of the new phenomenological nuclear potential introduced recently by ... more By adjusting the parameters of the new phenomenological nuclear potential introduced recently by P. Salamon and T. Vertse (2008) (SV) to the global potential sets of Perey and of Becchetti and Greenlees, it is shown that the SV potential well approximates the cut-off Woods--Saxon (CWS) form even if its second term is set to zero. The important difference between the CWS and SV potentials is that CWS jumps to zero at the cut-off radius, while the SV potential goes to zero smoothly. We fitted the single-term SV potential to the global potentials, and compared the spectra and the pole trajectories of neutron single-particle states generated by some light neutron-deficient nuclei that are most often used in positron emission tomography (PET): $^{13}$N, $^{15}$O and $^{18}$F. The CWS and the SV energies agree reasonably well, and only the pole trajectories, which span extremities, are substantially different.
An unified shell model scheme to evaluate simultaneously the contributions of bound singleparticl... more An unified shell model scheme to evaluate simultaneously the contributions of bound singleparticle states, Gamow resonances, antibound (virtual) states and continuum complex scattering states is presented. The formalism could be very suitable to study processes occurring in the continuum part of the nuclear spectra El espectro continuo de un sistema de muchos cuerpos presenta ciertas propiedades características de sistemas resonantes, como por ejemplo secciones eficaces con picos muy definidos a energías cercanas a la resonacia, o un cambio rápido en el desfasaje ("phase shift") a la energía de resonancia. Este estado resonante puede ser descripto, para resonancias angostas, aproximadamente por un vector de Gamow, esto es, un autovector generalizado del Hamiltoniano del sistema con energía compleja. Estas energías son polos de la extensión analítica de la matris S, como también lo son las energías correspodientes a los estados ligados. Además de estos polos la matris S tiene otros polos sobre el eje imaginario negativo. Los estados asociados con estos polos se los llama estados anti-ligados o estados virtuales. Cuando el polo está muy cerca del eje real produce efectos observables en la sección eficaz. En este trabajo mostramos como incluir tales estados en el modelo de capas y lo aplicamos a un sistema nuclear donde es conocido que tal efecto existe.
New isomeric states were identified in the dripline nucleus ^140Dy with a half-life of 7 mus[1,2]... more New isomeric states were identified in the dripline nucleus ^140Dy with a half-life of 7 mus[1,2] and in ^140Eu (t_1/2 = 300 ns) in an experiment at the focal plane of the RMS at HRIBF. The isomers were produced by bombardment of a 1 mg/cm^2 target of ^92Mo with 315 MeV ^54Fe. Level schemes have been constructed based on gamma-gamma
The parameters of the nuclear liquid drop model, such as the volume, surface, symmetry, and curva... more The parameters of the nuclear liquid drop model, such as the volume, surface, symmetry, and curvature constants, as well as bulk radii, are extracted from the non-relativistic and relativistic energy density functionals used in microscopic calculations for finite nuclei. The microscopic liquid drop energy, obtained self-consistently for a large sample of finite, spherical nuclei, has been expanded in terms of powers of A −1/3 (or inverse nuclear radius) and the isospin excess (or neutron-to-proton asymmetry). In order to perform a reliable extrapolation in the inverse radius, the calculations have been carried out for nuclei with huge numbers of nucleons, of the order of 10 6 . The Coulomb interaction has been ignored to be able to approach nuclei of arbitrary sizes and to avoid radial instabilities characteristic of systems with very large atomic numbers. The main contribution to the fluctuating part of the binding energy has been removed using the Green's function method to calculate the shell correction. The limitations of applying the leptodermous expansion to actual nuclei are discussed. While the leading terms in the macroscopic energy expansion can be extracted very precisely, the higher-order, isospin-dependent terms are prone to large uncertainties due to finite-size effects.
Shell corrections to the nuclear binding energy as a measure of shell effects in superheavy nucle... more Shell corrections to the nuclear binding energy as a measure of shell effects in superheavy nuclei are studied within the self-consistent Skyrme-Hartree-Fock and Relativistic Mean-Field theories. Due to the presence of low-lying proton continuum resulting in a free particle gas, special attention is paid to the treatment of single-particle level density. To cure the pathological behavior of shell correction around the particle threshold, the method based on the Green's function approach has been adopted. It is demonstrated that for the vast majority of Skyrme interactions commonly employed in nuclear structure calculations, the strongest shell stabilization appears for Z=124, and 126, and for N =184. On the other hand, in the relativistic approaches the strongest spherical shell effect appears systematically for Z=120 and N =172. This difference has probably its roots in the spin-orbit potential. We have also shown that, in contrast to shell corrections which are fairly independent on the force, macroscopic energies extracted from self-consistent calculations strongly depend on the actual force parametrisation used. That is, the A and Z dependence of mass surface when extrapolating to unknown superheavy nuclei is prone to significant theoretical uncertainties.
Shell corrections of the finite deformed Woods-Saxon potential are calculated using the Green's f... more Shell corrections of the finite deformed Woods-Saxon potential are calculated using the Green's function method and the generalized Strutinsky smoothing procedure. They are compared with the results of the standard prescription which are affected by the spurious contribution from the unphysical particle gas. In the new method, the shell correction approaches the exact limit provided that the dimension of the single-particle (harmonic oscillator) basis is sufficiently large. For spherical potentials, the present method is faster than the exact one in which the contribution from the particle continuum states is explicitly calculated. For deformed potentials, the Green's function method offers a practical and reliable way of calculating shell corrections for weakly bound nuclei.
Two methods the complex energy shell model (CXSM) and the complex scaling (CS) approach were used... more Two methods the complex energy shell model (CXSM) and the complex scaling (CS) approach were used for calculating isobaric analog resonances (IAR) in the Lane model. The IAR parameters calculated by the CXSM and the CS methods were checked against the parameters extracted from the direct numerical solution of the coupled channel Lane equations (CC). The agreement with the CC results was generally better than 1 keV for both methods and for each partial waves concerned.
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Papers by T. Vertse