renzo leonardi | University of Trento (original) (raw)
Papers by renzo leonardi
Lettere al Nuovo Cimento, 1969
It is interesting to observe that for the matrix ele] llents We have a quenching, or an antiquenc... more It is interesting to observe that for the matrix ele] llents We have a quenching, or an antiquenching (Fig. la)), effect. We expect therefore that the same mechanism is responsible for the quenching of both magnetic moments and matrix elements I:,~] I~ T:'I. 0.5 t-1
Il Nuovo Cimento B Series 10, 1969
Scuola Normale Superiore -Pisa (ricevuto iI 30 Settembre 1968)
Physics Letters B, 1994
Upper and lower bounds to the nucleon electric polarizability are discussed, within the constitue... more Upper and lower bounds to the nucleon electric polarizability are discussed, within the constituent quark model, by using a sum rule approach for the nucleon response to an external static electric field. We find that the SU(6) breaking terms of the quark-quark potential are important in order to evaluate the size and the electric response of the nucleon consistently and we discuss the role of the hyperfine interaction in some detail.
Nuclear Physics A, 2005
The goal of this article is to briefly present a few examples where nuclear methods * and instrum... more The goal of this article is to briefly present a few examples where nuclear methods * and instruments have been proven useful in analyzing paintings. In particular it will be illustrated how to: a) Discover a self portrait of Van Dyck with NEUTRONS. b) Unmask a forgery with PROTONS. c) Explore the mystery of silver point drawings with PROTONS. * A wide number of articles and conference proceedings have been dedicated to the subject and its various facets; listing them is beyond the scope of this article. Our goal is simply to stimulate those who never thought about the exciting applications of nuclear (and condensed matter) methods to works of art, to explore the dedicated literature. Nuclear Physics A 752 (2005) 659c-674c 0375-9474/$ -see front matter
Abstract The authorship of the MET Crucifixion, generally ascribed to Jan Van Eyck (JVE), has rec... more Abstract
The authorship of the MET Crucifixion, generally ascribed to Jan Van Eyck (JVE), has recently been questioned on the basis of astronomical arguments. In the following, it is argued that the “realistic” moon painted in the panel should be considered a typical Eyckian detail. JVE is the author of another astonishing moon, painted in the sky of the panel “Chevaliers du Christ” of the Ghent altarpiece. This panel offers the first truly detailed map of the moon relevant to the history of astronomy. In it, the most important “maria” are clearly identifiable. From the map, one can infer the libration parameters.
A realistically-painted moon appears also in two miniatures of the Hand G group. To the extent that these may be attributed to JVE and his workshop, it can be claimed that, in his skies and landscapes, JVE handled the moon with astronomical precision as early as 1420. When and how did JVE acquire his deep knowledge of the moon features?
The details of the moon are such as to suggest the use, during JVE’s astronomical observations, of some, at least rudimentary, magnifying optical system.
Abstract The authorship of the MET Crucifixion, generally ascribed to Jan Van Eyck (JVE), has rec... more Abstract
The authorship of the MET Crucifixion, generally ascribed to Jan Van Eyck (JVE), has recently been questioned on the basis of astronomical arguments. In the following, it is argued that the “realistic” moon painted in the panel should be considered a typical Eyckian detail. JVE is the author of another astonishing moon, painted in the sky of the panel “Chevaliers du Christ” of the Ghent altarpiece. This panel offers the first truly detailed map of the moon relevant to the history of astronomy. In it, the most important “maria” are clearly identifiable. From the map, one can infer the libration parameters.
A realistically-painted moon appears also in two miniatures of the Hand G group. To the extent that these may be attributed to JVE and his workshop, it can be claimed that, in his skies and landscapes, JVE handled the moon with astronomical precision as early as 1420. When and how did JVE acquire his deep knowledge of the moon features?
The details of the moon are such as to suggest the use, during JVE’s astronomical observations, of some, at least rudimentary, magnifying optical system.
Nuclear Physics A, 1978
The lineal' response of a nucleus in an external oscillating field has been studied in the framew... more The lineal' response of a nucleus in an external oscillating field has been studied in the framework of TDHF theory. The dynamic polarizability evaluated in TDHF theory has been related to RPA energies and matrix elements and a method to obtain RPA sum rules from the TDHF polarizability has been explicitly developed. This method can be applied to isoscalar as well as to isovector and spin excitations. Finally, a prescription to identify mass and restorting force parameters of various collective models with RPA sum rules is given.
Nuclear Physics A, 1978
The lineal' response of a nucleus in an external oscillating field has been studied in the framew... more The lineal' response of a nucleus in an external oscillating field has been studied in the framework of TDHF theory. The dynamic polarizability evaluated in TDHF theory has been related to RPA energies and matrix elements and a method to obtain RPA sum rules from the TDHF polarizability has been explicitly developed. This method can be applied to isoscalar as well as to isovector and spin excitations. Finally, a prescription to identify mass and restorting force parameters of various collective models with RPA sum rules is given.
Few-body Systems, 1999
Lower and upper bounds to the electric polarizability and para-magnetic susceptibility are expli... more Lower and upper bounds to the electric polarizability and para-magnetic susceptibility are explicitly calculated by means of a sum-rule technique and within a large variety of constituent quark models. The role of three-body forces in the potential model is investigated in detail as well as the effects of SU(6) breaking terms. The quark degrees of freedom give a quite sizeable contribution to the static polarizability and the meson cloud accounts roughly for 30% and 60% of the electric proton and neutron polarizability respectively. The quark contribution to the paramagnetic susceptibility is even higher and the mesonic effects are rather uncertain.
Physical Review Letters, 1976
We present a microscopic approach to the monopole and quadrupole isoscalar giant resonances based... more We present a microscopic approach to the monopole and quadrupole isoscalar giant resonances based on appropriate sum rules. The energies of both modes contain the same model-independent contribution (2ℏomega) and a contribution involving antisymmetrization effects and the nuclear potential. Several potentials are considered and the results of many other approaches are derived in a simple and compact way.
Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields, 1976
TheM1-transitions in nuclei are studied by means of sum rules. A useful sum rule for the total st... more TheM1-transitions in nuclei are studied by means of sum rules. A useful sum rule for the total strength of theM1-excitations is given in terms of the number of the nucleons which are in the nonfilledl-shell. The well-known Kurath sum rule for the energy-weighted total strength is generalized to include the two-body potential contribution. The centroid of the excitation is studied; finally the isotopic spreading of theT upper andT lower component of the excitation is analysed and the «symmetry energy» for theM1-transitions is studied. Not only the centroid shift, but also the isotopic splitting is an effect due toSU 4-breaking terms of the nuclear Hamiltonian, in particular the spinorbit, Bartlett, Heisenberg terms. Si studiano le transizioniM1 nei nuclei per mezzo di regole di somma. Si dà una utile regola di somma per l’intensità totale delle eccitazioniM1 in funzione del numero di nucleoni che sono negli stratil non totalmente riempiti. Si generalizza la ben conosciuta regola di somma di Kurath per includere il contributo del potenziale. Si studia il centroide dell’eccitazione e, da ultimo, si analizzano la separazione delle componentiT+1 eT della eccitazione e le «energie di simmetria» per le transizioniM1. Non soltanto lo spostamento del centroide, ma anche la separazione nei canali di spin isotopico è dovuta ai termini dell’hamiltoniana nucleare responsabili della rottura della simmetriaSU 4, in particolare dai termini spin-orbita, Bartlett ed Heisenberg. С помошью правил сумм исследуютсяM1 переходы в ядрах. Приво-дится полеэное правило сумм для полной интенсивностиM1 воэбуждений в тер-минах числа нуклонов, которые находятся на неэаполненнойl-оболочке. Хорощо иэвестное правило сумм Кирата для полной интенсивности обобшается, чтобы включить вклад двухчастичного потенциала. Исследуется воэбуждение центроида. Затем аналиэируется иэотопическое расщирениеT верхней иT нижней компонент воэбуждения и иэучается « знергия симметрии » дляM1 переходов. He только сдвиг центроида, но и иэотопическое расшепление обусловлены членами, нарущаю-шимиSU 4, в ядерном Гамильтониане, в частности, спин-орбитальными членами и членами Бартлета и Гайэенберга.
Physics Letters B, 1984
Energy weighted sum rules for Gamow-Teller and M1 excitations are evaluated in three double close... more Energy weighted sum rules for Gamow-Teller and M1 excitations are evaluated in three double closed nuclei (4He, 160, 4°Ca) with a phenomenologically correlated ground state. A strong dependence of these sum rules on tensor correlations is shown for Gamow Teller and magnetic dipole operators, both isoscalar and isovector.
Physical Review Letters, 1969
A systematic analysis of the electric dipole sum rules in the different isospin channels is given... more A systematic analysis of the electric dipole sum rules in the different isospin channels is given. The connections between these sum rules and the well-known old ones are classified. A simple application is given in resolving the isospin components of the nuclear giant resonance.
Physical Review Letters, 1970
Phenomenological analysis of Gamow-Teller transitions and magnetic moments is done for the ground... more Phenomenological analysis of Gamow-Teller transitions and magnetic moments is done for the ground states of the mirror nuclei, putting in evidence the linear quenching of the matrix elements <iAsigma3i> and <iAsigma3itau3i>. Configuration mixing techniques in the j-j coupling scheme are discussed and used to explain the quenching and to fit the experimental data.
Rivista Del Nuovo Cimento, 1969
Physical Review Letters, 1968
... ISOSPIN DOUBLETS Renzo Leonardi Istituto di Fisica dell'UniversitA di Bologna, Bologna, ... more ... ISOSPIN DOUBLETS Renzo Leonardi Istituto di Fisica dell'UniversitA di Bologna, Bologna, Italy and Marco Rosa-Clot Scuola Normale ... OF THE SC49 ANALOG LEVELS M. Divadeenam* Nuclear Structure Laboratory, Duke University, Durham, North Carolina and William P ...
Physics Letters B, 1970
We study the energy dependence of the first forbidden Fermi and Gamov Teller matrix elements, usi... more We study the energy dependence of the first forbidden Fermi and Gamov Teller matrix elements, using sum rule techniques which give us a simple tool for the evaluation of the SU(4) breaking effect. A satisfactory agreement with experimental data is obtained.
Physical Review C, 1972
We study with sum-rule techniques nuclear neutrino-induced reactions in the limit in which these ... more We study with sum-rule techniques nuclear neutrino-induced reactions in the limit in which these reactions involve mainly giant-resonance excitation (i.e., at small angles). Resonant excitation is particularly important because simple shell-model and Fermi-gas calculations appear to give results which are too low relative to experiment for the differential cross section at small angles. Furthermore, in the strictly forward scattering region,
Lettere al Nuovo Cimento, 1969
It is interesting to observe that for the matrix ele] llents We have a quenching, or an antiquenc... more It is interesting to observe that for the matrix ele] llents We have a quenching, or an antiquenching (Fig. la)), effect. We expect therefore that the same mechanism is responsible for the quenching of both magnetic moments and matrix elements I:,~] I~ T:'I. 0.5 t-1
Il Nuovo Cimento B Series 10, 1969
Scuola Normale Superiore -Pisa (ricevuto iI 30 Settembre 1968)
Physics Letters B, 1994
Upper and lower bounds to the nucleon electric polarizability are discussed, within the constitue... more Upper and lower bounds to the nucleon electric polarizability are discussed, within the constituent quark model, by using a sum rule approach for the nucleon response to an external static electric field. We find that the SU(6) breaking terms of the quark-quark potential are important in order to evaluate the size and the electric response of the nucleon consistently and we discuss the role of the hyperfine interaction in some detail.
Nuclear Physics A, 2005
The goal of this article is to briefly present a few examples where nuclear methods * and instrum... more The goal of this article is to briefly present a few examples where nuclear methods * and instruments have been proven useful in analyzing paintings. In particular it will be illustrated how to: a) Discover a self portrait of Van Dyck with NEUTRONS. b) Unmask a forgery with PROTONS. c) Explore the mystery of silver point drawings with PROTONS. * A wide number of articles and conference proceedings have been dedicated to the subject and its various facets; listing them is beyond the scope of this article. Our goal is simply to stimulate those who never thought about the exciting applications of nuclear (and condensed matter) methods to works of art, to explore the dedicated literature. Nuclear Physics A 752 (2005) 659c-674c 0375-9474/$ -see front matter
Abstract The authorship of the MET Crucifixion, generally ascribed to Jan Van Eyck (JVE), has rec... more Abstract
The authorship of the MET Crucifixion, generally ascribed to Jan Van Eyck (JVE), has recently been questioned on the basis of astronomical arguments. In the following, it is argued that the “realistic” moon painted in the panel should be considered a typical Eyckian detail. JVE is the author of another astonishing moon, painted in the sky of the panel “Chevaliers du Christ” of the Ghent altarpiece. This panel offers the first truly detailed map of the moon relevant to the history of astronomy. In it, the most important “maria” are clearly identifiable. From the map, one can infer the libration parameters.
A realistically-painted moon appears also in two miniatures of the Hand G group. To the extent that these may be attributed to JVE and his workshop, it can be claimed that, in his skies and landscapes, JVE handled the moon with astronomical precision as early as 1420. When and how did JVE acquire his deep knowledge of the moon features?
The details of the moon are such as to suggest the use, during JVE’s astronomical observations, of some, at least rudimentary, magnifying optical system.
Abstract The authorship of the MET Crucifixion, generally ascribed to Jan Van Eyck (JVE), has rec... more Abstract
The authorship of the MET Crucifixion, generally ascribed to Jan Van Eyck (JVE), has recently been questioned on the basis of astronomical arguments. In the following, it is argued that the “realistic” moon painted in the panel should be considered a typical Eyckian detail. JVE is the author of another astonishing moon, painted in the sky of the panel “Chevaliers du Christ” of the Ghent altarpiece. This panel offers the first truly detailed map of the moon relevant to the history of astronomy. In it, the most important “maria” are clearly identifiable. From the map, one can infer the libration parameters.
A realistically-painted moon appears also in two miniatures of the Hand G group. To the extent that these may be attributed to JVE and his workshop, it can be claimed that, in his skies and landscapes, JVE handled the moon with astronomical precision as early as 1420. When and how did JVE acquire his deep knowledge of the moon features?
The details of the moon are such as to suggest the use, during JVE’s astronomical observations, of some, at least rudimentary, magnifying optical system.
Nuclear Physics A, 1978
The lineal' response of a nucleus in an external oscillating field has been studied in the framew... more The lineal' response of a nucleus in an external oscillating field has been studied in the framework of TDHF theory. The dynamic polarizability evaluated in TDHF theory has been related to RPA energies and matrix elements and a method to obtain RPA sum rules from the TDHF polarizability has been explicitly developed. This method can be applied to isoscalar as well as to isovector and spin excitations. Finally, a prescription to identify mass and restorting force parameters of various collective models with RPA sum rules is given.
Nuclear Physics A, 1978
The lineal' response of a nucleus in an external oscillating field has been studied in the framew... more The lineal' response of a nucleus in an external oscillating field has been studied in the framework of TDHF theory. The dynamic polarizability evaluated in TDHF theory has been related to RPA energies and matrix elements and a method to obtain RPA sum rules from the TDHF polarizability has been explicitly developed. This method can be applied to isoscalar as well as to isovector and spin excitations. Finally, a prescription to identify mass and restorting force parameters of various collective models with RPA sum rules is given.
Few-body Systems, 1999
Lower and upper bounds to the electric polarizability and para-magnetic susceptibility are expli... more Lower and upper bounds to the electric polarizability and para-magnetic susceptibility are explicitly calculated by means of a sum-rule technique and within a large variety of constituent quark models. The role of three-body forces in the potential model is investigated in detail as well as the effects of SU(6) breaking terms. The quark degrees of freedom give a quite sizeable contribution to the static polarizability and the meson cloud accounts roughly for 30% and 60% of the electric proton and neutron polarizability respectively. The quark contribution to the paramagnetic susceptibility is even higher and the mesonic effects are rather uncertain.
Physical Review Letters, 1976
We present a microscopic approach to the monopole and quadrupole isoscalar giant resonances based... more We present a microscopic approach to the monopole and quadrupole isoscalar giant resonances based on appropriate sum rules. The energies of both modes contain the same model-independent contribution (2ℏomega) and a contribution involving antisymmetrization effects and the nuclear potential. Several potentials are considered and the results of many other approaches are derived in a simple and compact way.
Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields, 1976
TheM1-transitions in nuclei are studied by means of sum rules. A useful sum rule for the total st... more TheM1-transitions in nuclei are studied by means of sum rules. A useful sum rule for the total strength of theM1-excitations is given in terms of the number of the nucleons which are in the nonfilledl-shell. The well-known Kurath sum rule for the energy-weighted total strength is generalized to include the two-body potential contribution. The centroid of the excitation is studied; finally the isotopic spreading of theT upper andT lower component of the excitation is analysed and the «symmetry energy» for theM1-transitions is studied. Not only the centroid shift, but also the isotopic splitting is an effect due toSU 4-breaking terms of the nuclear Hamiltonian, in particular the spinorbit, Bartlett, Heisenberg terms. Si studiano le transizioniM1 nei nuclei per mezzo di regole di somma. Si dà una utile regola di somma per l’intensità totale delle eccitazioniM1 in funzione del numero di nucleoni che sono negli stratil non totalmente riempiti. Si generalizza la ben conosciuta regola di somma di Kurath per includere il contributo del potenziale. Si studia il centroide dell’eccitazione e, da ultimo, si analizzano la separazione delle componentiT+1 eT della eccitazione e le «energie di simmetria» per le transizioniM1. Non soltanto lo spostamento del centroide, ma anche la separazione nei canali di spin isotopico è dovuta ai termini dell’hamiltoniana nucleare responsabili della rottura della simmetriaSU 4, in particolare dai termini spin-orbita, Bartlett ed Heisenberg. С помошью правил сумм исследуютсяM1 переходы в ядрах. Приво-дится полеэное правило сумм для полной интенсивностиM1 воэбуждений в тер-минах числа нуклонов, которые находятся на неэаполненнойl-оболочке. Хорощо иэвестное правило сумм Кирата для полной интенсивности обобшается, чтобы включить вклад двухчастичного потенциала. Исследуется воэбуждение центроида. Затем аналиэируется иэотопическое расщирениеT верхней иT нижней компонент воэбуждения и иэучается « знергия симметрии » дляM1 переходов. He только сдвиг центроида, но и иэотопическое расшепление обусловлены членами, нарущаю-шимиSU 4, в ядерном Гамильтониане, в частности, спин-орбитальными членами и членами Бартлета и Гайэенберга.
Physics Letters B, 1984
Energy weighted sum rules for Gamow-Teller and M1 excitations are evaluated in three double close... more Energy weighted sum rules for Gamow-Teller and M1 excitations are evaluated in three double closed nuclei (4He, 160, 4°Ca) with a phenomenologically correlated ground state. A strong dependence of these sum rules on tensor correlations is shown for Gamow Teller and magnetic dipole operators, both isoscalar and isovector.
Physical Review Letters, 1969
A systematic analysis of the electric dipole sum rules in the different isospin channels is given... more A systematic analysis of the electric dipole sum rules in the different isospin channels is given. The connections between these sum rules and the well-known old ones are classified. A simple application is given in resolving the isospin components of the nuclear giant resonance.
Physical Review Letters, 1970
Phenomenological analysis of Gamow-Teller transitions and magnetic moments is done for the ground... more Phenomenological analysis of Gamow-Teller transitions and magnetic moments is done for the ground states of the mirror nuclei, putting in evidence the linear quenching of the matrix elements <iAsigma3i> and <iAsigma3itau3i>. Configuration mixing techniques in the j-j coupling scheme are discussed and used to explain the quenching and to fit the experimental data.
Rivista Del Nuovo Cimento, 1969
Physical Review Letters, 1968
... ISOSPIN DOUBLETS Renzo Leonardi Istituto di Fisica dell'UniversitA di Bologna, Bologna, ... more ... ISOSPIN DOUBLETS Renzo Leonardi Istituto di Fisica dell'UniversitA di Bologna, Bologna, Italy and Marco Rosa-Clot Scuola Normale ... OF THE SC49 ANALOG LEVELS M. Divadeenam* Nuclear Structure Laboratory, Duke University, Durham, North Carolina and William P ...
Physics Letters B, 1970
We study the energy dependence of the first forbidden Fermi and Gamov Teller matrix elements, usi... more We study the energy dependence of the first forbidden Fermi and Gamov Teller matrix elements, using sum rule techniques which give us a simple tool for the evaluation of the SU(4) breaking effect. A satisfactory agreement with experimental data is obtained.
Physical Review C, 1972
We study with sum-rule techniques nuclear neutrino-induced reactions in the limit in which these ... more We study with sum-rule techniques nuclear neutrino-induced reactions in the limit in which these reactions involve mainly giant-resonance excitation (i.e., at small angles). Resonant excitation is particularly important because simple shell-model and Fermi-gas calculations appear to give results which are too low relative to experiment for the differential cross section at small angles. Furthermore, in the strictly forward scattering region,