Effective charged neutrons involved in one- and two- nucleon tunneling processes in heavy ion collisions between superfluid nuclei are expected to emit photons. Although the centroid, width and integrated energy area characterizing the associated gamma-strength functions are rather similar, the corresponding line shapes reflect the thermal equilibrated-like character of the quasiparticle transfer (1n-channel, blackbody spectral functional dependence), and the quantal coherent character of the Cooper pair transfer (2n-channel, Gaussian functional dependence) respectively. The predicted angular distributions, polarizations and analyzing power provide further insight into the profoundly different physics to be found at the basis of what can be considered a transient Joule-like and a (ac) Josephson-like nuclear processes

Josephson-like junctions, transiently established in heavy ion collisions between superfluid nuclei, few MeV below the Coulomb barrier, allow for the back and forth transfer of a nuclear Cooper pair of effectively charged nucleons and thus the emission of γ-rays. The semiclassical description of single Cooper pair alternating current is shown to contain the gauge phases and gauge rotational frequencies as required by the Josephson (ac) effect, in keeping with the derivation of the transfer (tunneling) Hamiltonian in a gauge invariant representation. The fact that such reaction description is equivalent to a second order DWBA T -matrix formulation extensively used in the study of pairing rotational bands with two-particle transfer reactions, together with the nuclear structure result that the Bardeen-Cooper-Schrieffer (BCS) condensation order parameter α0 = ∑ ν>0 UνVν (number of Cooper pairs), sum of the coherence factors UνVν (proportional to the two-nucleon transfer spectroscopic amplitudes), is quite stable with respect to model description, is found to be connected with the emergence of two strongly convergent parameters (conserved quantities) within the time the abnormal densities of the two superfluid nuclei overlap: a) the correlation length (dc); b) the number of emitted γ-rays per cycle (ac), and thus the dipole moment of the successively transferred nucleons. Result which leads to a nuclear parallel with the direct current (dc) and alternating current (ac) Josephson effects, and which testifies to the validity of BCS theory of superconductivity down to few Cooper pair condensates, and single Cooper pair alternating currents. The physics at the basis of a quantitative description of Cooper pair tunneling between weakly coupled superconductors or superfluid nuclei at energies below the Coulomb barrier, is that the process is dominated by the successive transfer of the two partner fermions entangled over distances of the order of the coherence length, ≈ 104Å in the case of lead, and 13.5 fm in the case of the reaction 116Sn +60 Ni →114 Sn(gs) +62 Ni(gs) at few MeV below the Coulomb barrier.

This monograph presents a unified theory of nuclear structure and nuclear reactions in the language of quantum electrodynamics, Feynman diagrams. It describes how two-nucleon transfer reaction processes can be used as a quantitative tool to interpret experimental findings with the help of computer codes and nuclear field theory. Making use of Cooper pair transfer processes, the theory is applied to the study of pair correlations in both stable and unstable exotic nuclei. Special attention is given to unstable, exotic halo systems, which lie at the forefront of the nuclear physics research being carried out at major laboratories around the world. This volume is distinctive in dealing in both nuclear structure and reactions and benefits from comparing the nuclear field theory with experimental observables, making it a valuable resource for incoming and experienced researchers who are working in nuclear pairing and using transfer reactions to probe them.

Transient Weak Links between Superconducting Nuclei: Coherence Length R. A. Broglia1, F. Barranco2, G. Potel3, and E. Vigezzi4 1The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Blegdamsvej 17, Denmark; Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, I-20133 Milano, Italy 2Departamento de Fı́sica Aplicada III, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos, Sevilla, Spain 3Lawrence Livermore National Laboratory, Livermore, California 94550, USA 4INFN Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy

R. A. Broglia,1, 2 F. Barranco,3 G. Potel,4 and E. Vigezzi5 1The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Blegdamsvej 17, Denmark 2Dipertimento di Fisica, Università degli Studi di Milano, Via Celoria 16, I-20133 Milano, Italy 3Departamento de Fı́sica Aplicada III, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos, Sevilla, Spain 4Lawrence Livermore National Laboratory, Livermore, California 94550, USA 5INFN Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy (Dated: March 26, 2021)

The denatured state of several proteins has been shown to display transient structures that are relevant for folding, stability, and aggregation. To detect them by nuclear magnetic resonance (NMR) spectroscopy, the denatured state must be stabilized by chemical agents or changes in temperature. This makes the environment different from that experienced in biologically relevant processes. Using high-resolution heteronuclear NMR spectroscopy, we have characterized several denatured states of a monomeric variant of HIV-1 protease, which is natively structured in water, induced by different concentrations of urea, guanidinium chloride, and acetic acid. We have extrapolated the chemical shifts and the relaxation parameters to the denaturant-free denatured state at native conditions, showing that they converge to the same values. Subsequently, we characterized the conformational properties of this biologically relevant denatured state under native conditions by advanced molecular dynamics simulations and validated the results by comparison to experimental data. We show that the denatured state of HIV-1 protease under native conditions displays rich patterns of transient native and non-native structures, which could be of relevance to its guidance through a complex folding process.

While Josephson-like junctions, transiently established in heavy-ion collisions (tau(coll) 10(-21) s) between superfluid nuclei-through which Cooper-pair tunneling (Q-value Q(2n)) proceeds mainly in terms of successive transfer of entangled nucleons-is deprived from the macroscopic aspects of a supercurrent, it displays many of the special effects associated with spontaneous symmetry breaking in gauge space (BCS condensation), which can be studied in terms of individual quantum states and of tunneling of single Cooper pairs. From the results of studies of one- and two-neutron transfer reactions carried out at energies below the Coulomb barrier we estimate the value of the mean-square radius (correlation length) of the nuclear Cooper pair. A quantity related to the largest distance of closest approach for which the absolute two-nucleon tunneling cross section is of the order of the single-particle one. Furthermore, emission of gamma rays of (Josephson) frequency v(J) = Q(2n)/h distributed over an energy range h/tau(coll) is predicted.

This monograph presents a unified theory of nuclear structure and nuclear reactions in the language of quantum electrodynamics, Feynman diagrams. It describes how two-nucleon transfer reaction processes can be used as a quantitative tool to interpret experimental findings with the help of computer codes and nuclear field theory. Making use of Cooper pair transfer processes, the theory is applied to the study of pair correlations in both stable and unstable exotic nuclei. Special attention is given to unstable, exotic halo systems, which lie at the forefront of the nuclear physics research being carried out at major laboratories around the world. This volume is distinctive in dealing in both nuclear structure and reactions and benefits from comparing the nuclear field theory with experimental observables, making it a valuable resource for incoming and experienced researchers who are working in nuclear pairing and using transfer reactions to probe them.

We show, within the framework of renormalized nuclear field theory and of the induced reaction surrogate formalism, that the highly debated Li-10 structure, studied in a recent high statistics Li-9(d, p) Li-10 one-neutron transfer experiment, is consistent with, or better, requires, the presence of a virtual 1/2(+) state of similar single-particle strength than that of the 1/2(-) resonance at 0.45 +/- 0.03 MeV. Based on continuum spectroscopy self-energy techniques, we find that the physical mechanism responsible for parity inversion in Li-10(3) is the same as that at the basis of the similar phenomenon observed in Be-11(4) and as that needed in Li-11 to have an important s-wave ground-state component. In particular the strong dynamical coupling between the s(1/2) and the d(5/2) states, mediated by the quadrupole vibration of the core Li-9. A phenomenon which also affects the strength distribution of the d(5/2) state, in particular, in the energy range of 3-4.5 MeV. Furthermore, this mechanism is also consistent with the (normal) sequence of the (1)p(1/2) and (2)s(1/2) levels in the N = 7 isotones B-12(5) and C-13(6). The main aim of the present Rapid Communication is that of treating structure and reactions on equal footing and in a common language. In other words, the calculation of the Li-9(d, p) Li-10 reaction as a single conceptual step from individual single-particle motion and collective vibrations to absolute double differential cross sections of renormalized virtual and resonant final states, which can be directly compared with experiment.

We show, within the framework of renormalized nuclear field theory and of the induced reaction surrogate formalism, that the highly debated $^{10}\mathrm{Li}$ structure, studied in a recent high statistics $^{9}\mathrm{Li}(d,p)\phantom{\rule{0.16em}{0ex}}^{10}\mathrm{Li}$ one-neutron transfer experiment, is consistent with, or better, requires, the presence of a virtual $1/{2}^{+}$ state of similar single-particle strength than that of the $1/{2}^{\ensuremath{-}}$ resonance at $0.45\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$. Based on continuum spectroscopy self-energy techniques, we find that the physical mechanism responsible for parity inversion in $_{3}^{10}\mathrm{Li}$ is the same as that at the basis of the similar phenomenon observed in $_{4}^{11}\mathrm{Be}$ and as that needed in $^{11}\mathrm{Li}$ to have an important $s$-wave ground-state component. In particular the strong dynamical coupling between the ${s}_{1/2}$ and the ${d}_{5/2}$ states, mediated by the quadrupole vibration of the core $^{9}\mathrm{Li}$. A phenomenon which also affects the strength distribution of the ${d}_{5/2}$ state, in particular, in the energy range of 3--4.5 MeV. Furthermore, this mechanism is also consistent with the (normal) sequence of the $1{p}_{1/2}$ and $2{s}_{1/2}$ levels in the $N=7$ isotones $_{5}^{12}\mathrm{B}$ and $_{6}^{13}\mathrm{C}$. The main aim of the present Rapid Communication is that of treating structure and reactions on equal footing and in a common language. In other words, the calculation of the $^{9}\mathrm{Li}(d,p)^{10}\mathrm{Li}$ reaction as a single conceptual step from individual single-particle motion and collective vibrations to absolute double differential cross sections of renormalized virtual and resonant final states, which can be directly compared with experiment.

The interplay of particle and vibrations in N=7 isotones is considered according to nuclear field theory, focusing on the main many-body effects which renormalise the energy spectrum of the halo nucleus 11Be, leading to parity inversion and to renormalization of the form facto s determining the cross sections associated with one-nucleon transfer reactions.

The properties of the two-quasiparticle-like soft E1-modes and Pygmy Dipole Resonances (PDR) have been and are systematically studied with the help of inelastic and electromagnetic experiments which essentially probe the particle-hole components of these vibrations. It is shown that further insight in their characterisation can be achieved with the help of two-nucleon transfer reactions, in particular concerning the particle-particle components of the modes, in terms of absolute differential cross sections which take properly into account successive and simultaneous transfer mechanisms corrected for non-orthogonality, able to reproduce the experimental findings at the 10% level. The process 9Li(t, p)11Li(1-) is discussed, and absolute cross sections predicted.

The present volume is, in keeping with its title, divided into four sections, in each of which one finds contributions from world specialists, covering a wide variety of subjects lying at the forefront of nuclear research.Quoting from the first scientific contribution, the articles of the present special issue are dedicated to the memory of Pier Francesco Bortignon and devoted to developments related to his pioneering ideas.In this contribution, results of relativistic nuclear field theory at finite temperature, with special emphasis on damping phenomena are presented.These are subjects to which Pier Francesco dedicated much effort and provided equally much insight, especially concerning the role doorway states play in the damping of collective motion in general, and of giant resonances in particular.Also concerning the damping due to the decay into individual particle-hole excitations (Landau damping) discussed in detail in another contribution to the first section, in connection with the analysis of the gross, intermediate and fine structure of giant resonances.Moving to the second section dealing with pygmy resonances, not surprisingly a very rich section, we are confronted, among many other contributions, with an overview of selected experimental work on the gamma-decay from the GDR and the PDR, which acknowledges inspiration provided by Pier Francesco through the years, in particular concerning the problem of isospin symmetry in nuclei at finite temperature and of pygmy states far from stability.Within this context, another experimental contribution which concentrates on light exotic halo nuclei refers, in connection with 11 Li, to nuclear field theory calculations of Pier Francesco and collaborators, providing a simultaneous description of both the soft E1-mode (pygmy) and the strong mixing of s-and p-waves in the ground state.Coming to the third section, one reads about the observation of Giant Pairing Vibrations not in heavy, as expected, but in light nuclei.In connection with the ensuing elaboration of such a result, work of Pier Francesco is referred to in which a possible explanation is suggested, based on the much larger width expected for GPV in heavy nuclei as compared with light nuclei.The last section, reflecting its title, is more inhomogeneous than the three previous ones.Nonetheless, there is a red thread going through almost all of the contributions, namely nuclear field theory, particle-vibration coupling mechanism and doorway damping, subjects which lay at the center of Pier Francesco interests, and to which he so extensively and eminently contributed.Not only do the subjects in the different contributions honor the memory of Pier Francesco, but also the scientific and professional level with which they are treated constitutes a most proper tribute to the never-ceasing quest for accuracy which was characteristic of Pier Francesco's scientific endeavor.