Showing papers in "European Physical Journal A in 2015"

Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order

Abstract: We present improved nucleon-nucleon potentials derived in chiral effective field theory up to next-to-next-to-next-to-leading order. We argue that the nonlocal momentum-space regulator employed in the two-nucleon potentials of previous works (Nucl. Phys. A 747, 362 (2005) and Phys. Rev. C 68, 041001 (2003)) is not the most efficient choice, in particular since it affects the long-range part of the interaction. We are able to significantly reduce finite-cutoff artefacts by using an appropriate regularization in coordinate space which maintains the analytic structure of the amplitude. The new potentials do not require the additional spectral function regularization employed in (Nucl. Phys. A 747, 362 (2005)) to cut off the short-range components of the two-pion exchange and make use of the low-energy constants ci and di determined from pion-nucleon scattering without any fine tuning. We discuss in detail the construction of the new potentials and convergence of the chiral expansion for two-nucleon observables. We also employ a simple approach for estimating the theoretical uncertainty in few-nucleon calculations from the truncation of the chiral expansion that replaces previous reliance on cutoff variation.

The structure of the nucleon: Elastic electromagnetic form factors

Abstract: Precise proton and neutron form factor measurements at Jefferson Lab, using spin observables, have recently made a significant contribution to the unraveling of the internal structure of the nucleon. Accurate experimental measurements of the nucleon form factors are a test-bed for understanding how the nucleon’s static properties and dynamical behavior emerge from QCD, the theory of the strong interactions between quarks. There has been enormous theoretical progress, since the publication of the Jefferson Lab proton form factor ratio data, aiming at reevaluating the picture of the nucleon. We will review the experimental and theoretical developments in this field and discuss the outlook for the future.

Phenomenology of Pc(4380)+, Pc(4450)+ and related states

Abstract: The $ P_{c}(4380)^{+}$ and $ P_{c}(4450)^{+}$ states recently discovered at LHCb have masses close to several relevant thresholds, which suggests they can be described in terms of meson-baryon degrees of freedom. This article explores the phenomenology of these states, and their possible partners, from this point of view. Competing models can be distinguished by the masses of the neutral partners which have yet to be observed, and the existence or otherwise of further partners with different isospin, spin, and parity. Future experimental studies in different decay channels can also discriminate among models, using selection rules and algebraic relations among decays. Among the several possible meson-baryon pairs which could be important, one implies that the states are mixtures of isospins 1/2 and 3/2, with characteristic signatures in production and decay. A previous experimental study of a Cabibbo-suppressed decay showed no evidence for the states, and further analysis is required to establish the significance of this non-observation. Several intriguing similarities suggest that $ P_{c}(4450)^{+}$ is related to the $ X(3872)$ meson.

Constraints on the chiral unitary \(\bar KN\) amplitude from πΣK+ photoproduction data

Abstract: A chiral unitary approach for antikaon-nucleon scattering in on-shell factorization is studied. We find multiple sets of parameters for which the model describes all existing hadronic data similarly well. We confirm the two-pole structure of the Λ(1405). The narrow Λ(1405) pole appears at comparable positions in the complex energy plane, whereas the location of the broad pole suffers from a large uncertainty. In the second step, we use a simple model for photoproduction of K + πΣ off the proton and confront it with the experimental data from the CLAS Collaboration. It is found that only a few of the hadronic solutions allow for a consistent description of the CLAS data within the assumed reaction mechanism.

Prospective study on microscopic potential with Gogny interaction

Abstract: We present our current studies and future plans on microscopic potential based on effective nucleon-nucleon interaction and many-body theory. This framework treats in an unified way nuclear structure and reaction. It offers the opportunity to link the underlying effective interaction to nucleon scattering observables. The more consistently connected to a variety of reaction and structure experimental data the framework is, the more constrained the effective interaction will be. As a proof of concept, we present some recent results for both neutron and proton scattered from spherical target nucleus, namely 40Ca , using the Gogny D1S interaction. Possible fruitful cross-talks between microscopic potential, phenomenological potential and effective interaction are exposed. We then draw some prospective plans for the forthcoming years including scattering from spherical nuclei experiencing pairing correlations, scattering from axially deformed nuclei, and new effective interaction with reaction constraints.

The fundamental role of fission during r-process nucleosynthesis in neutron star mergers

Abstract: The rapid neutron-capture process, or r-process, is known to be of fundamental importance for explaining the origin of approximately half of the A > 60 stable nuclei observed in nature. Despite important efforts, the astrophysical site of the r-process remains unidentified. Here we study r-process nucleosynthesis in a material that is dynamically ejected by tidal and pressure forces during the merging of binary neutron stars. r-process nucleosynthesis during the decompression is known to be largely insensitive to the detailed astrophysical conditions because of efficient fission recycling, producing a composition that closely follows the solar r-abundance distribution for nuclei with mass numbers A > 140. Due to the important role played by fission in such a scenario, the impact of fission is carefully analyzed. We consider different state-of-the-art global models for the determination of the fission paths, nuclear level densities at the fission saddle points and fission fragment distributions. Based on such models, the sensitivity of the calculated r-process abundance distribution is studied. The fission path is found to strongly affect the region of heavy nuclei responsible for the fission recycling, while the fission fragment distribution of nuclei along the A ≃ 278 isobars defines the abundance pattern of nuclei produced in the 110 ≲ A ≲ 170 region. The late capture of prompt fission neutrons is also shown to affect the abundance distribution, and in particular the shape of the third r-process peak around A ≃ 195.

Fission modelling with FIFRELIN

Abstract: The nuclear fission process gives rise to the formation of fission fragments and emission of particles $ (n,\gamma , e^{-})$ . The particle emission from fragments can be prompt and delayed. We present here the methods used in the FIFRELIN code, which simulates the prompt component of the de-excitation process. The methods are based on phenomenological models associated with macroscopic and/or microscopic ingredients. Input data can be provided by experiment as well as by theory. The fission fragment de-excitation can be performed within Weisskopf (uncoupled neutron and gamma emission) or a Hauser-Feshbach (coupled neutron/gamma emission) statistical theory. We usually consider five free parameters that cannot be provided by theory or experiments in order to describe the initial distributions required by the code. In a first step this set of parameters is chosen to reproduce a very limited set of target observables. In a second step we can increase the statistics to predict all other fission observables such as prompt neutron, gamma and conversion electron spectra but also their distributions as a function of any kind of parameters such as, for instance, the neutron, gamma and electron number distributions, the average prompt neutron multiplicity as a function of fission fragment mass, charge or kinetic energy, and so on. Several results related to different fissioning systems are presented in this work. The goal in the next decade will be i) to replace some macroscopic ingredients or phenomenological models by microscopic calculations when available and reliable, ii) to be a support for experimentalists in the design of detection systems or in the prediction of necessary beam time or count rates with associated statistics when measuring fragments and emitted particle in coincidence iii) extend the model to be able to run a calculation when no experimental input data are available, iv) account for multiple chance fission and gamma emission before fission, v) account for the scission neutrons. Several efforts have already been made to replace macroscopic ingredients and phenomenology by microscopic ingredients provided in various nuclear parameter libraries such as electric dipole photon strength functions or HFB level densities. First results relative to theses aspects are presented in this work.

Investigation of ΛQ and ΞQ baryons in the heavy quark-light diquark picture

Abstract: We apply a new mass formula which is derived analytically in the relativistic flux tube model to the mass spectra of Λ Q and Ξ Q (Q = c or b quark) baryons. To this end, the heavy quark-light diquark picture is employed. We find that all masses of the available Λ Q and Ξ Q states can be understood well. The assignments to these states do not appear to contradict the strong decay properties. Λ c (2760)+ and Ξ c (2980) are assigned to the first radial excitations with J P = 1/2+. Λ c (2940)+ and Ξ c (3123) might be the 2P states. The Λ c (2880)+ and Ξ c(3080) are the good 1D candidates with J P = 5/2+. Λ c (3055) is likely to be a 1D state with J P =3/2+. Λ b (5912)0 and Λ b (5920)0 favor the 1P assignments with J P = 1/2− and 3/2−, respectively. We propose a search for the $$\tilde \Lambda _{c2} (5/2^ - )$$ state which can help to distinguish the diquark and three-body schemes.

Heavy-ion double charge exchange reactions: A tool toward $0 \nu\beta\beta$ nuclear matrix elements

Abstract: The knowledge of the nuclear matrix elements for the neutrinoless double beta decay is fundamental for neutrino physics. In this paper, an innovative technique to extract information on the nuclear matrix elements by measuring the cross section of a double charge exchange nuclear reaction is proposed. The basic point is that the initial- and final-state wave functions in the two processes are the same and the transition operators are similar. The double charge exchange cross sections can be factorized in a nuclear structure term containing the matrix elements and a nuclear reaction factor. First pioneering experimental results for the 40Ca(18O,18Ne)40Ar reaction at 270 MeV incident energy show that such cross section factorization reasonably holds for the crucial 0+ $ \rightarrow$ 0+ transition to 40Args, at least at very forward angles.

Eta photoproduction in a combined analysis of pion- and photon-induced reactions

Abstract: The ηN final state is isospin-selective and thus provides access to the spectrum of excited nucleons without being affected by excited Δ states. To this end, the world database on eta photoproduction off the proton up to a center-of-mass energy of E ∼ 2.3 GeV is analyzed, including data on differential cross sections, and single- and double-polarization observables. The resonance spectrum and its properties are determined in a combined analysis of eta and pion photoproduction off the proton together with the reactions πN → πN, ηN, KΛ and KΣ. For the analysis, the so-called Julich coupled-channel framework is used, incorporating unitarity, analyticity, and effective three-body channels. Parameters tied to photoproduction and hadronic interactions are varied simultaneously. The influence of recent MAMI T and F asymmetry data on the eta photoproduction amplitude is discussed in detail.

The quark-gluon vertex in Landau gauge bound-state studies

Abstract: We present a practical method for the solution of the quark-gluon vertex for use in Bethe-Salpeter and Dyson-Schwinger calculations. The efficient decomposition into the necessary covariants is detailed, with the numerical algorithm outlined for both real and complex Euclidean momenta. A truncation of the quark-gluon vertex, that neglects explicit back-coupling to enable the application to bound-state calculations, is given together with results for the quark propagator and quark-gluon vertex for different quark flavours. The relative impact of the various components of the quark-gluon vertex is highlighted with the flavour dependence of the effective quark-gluon interaction obtained, thus providing insight for the construction of phenomenological models within the rainbow ladder. Finally, we solve the corresponding Green's functions for complex Euclidean momenta as required in future bound-state calculations.

Gamma decay of pygmy states from inelastic scattering of ions

Abstract: An overview of relevant results on the study of 1− states focusing on their excitation with nuclear probes is given. Results obtained for the 90Zr , 124Sn , and 208Pb nuclei using the (17O,17O′γ) reaction are compared with available data obtained with the (γ, γ′, and (p, p′) reactions. These comparisons allow to learn on the nature of the populated states, particularly the E1 states, whose isospin character is presently poorly known. The DWBA description of the data is discussed in terms of different form factors, standard collective form factor and form factors obtained by folding microscopically calculated transition densities. The relevant aspects related to the used theoretical approach are also presented. The main objective of the analyses is the extraction of the values of the fraction of the energy weighted sum rule strength for the isoscalar dipole excitation. For completeness, in all cases, the DWBA analysis was made also for the excitations of 2+ and 3− states.

Spectra of heavy mesons in the Bethe-Salpeter approach

Abstract: We present a calculation of the spectrum of charmonia, bottomonia and Bc-meson states with “ordinary” and exotic quantum numbers. We discuss the merits and limitations of a rainbow-ladder truncation of Dyson-Schwinger and Bethe-Salpeter equations and explore the effects of different shapes of the effective running coupling on ground and excited states in channels with quantum numbers $J\le 3$ . We furthermore discuss the status of the $X(3872)$ as a potential (excited) quark-antiquark state and give predictions for the masses of charmonia and bottomonia in the tensor channels with $J= 2, 3$ .

Subtracted dispersion relation formalism for the two-photon exchange correction to elastic electron-proton scattering: Comparison with data

Abstract: We apply a subtracted dispersion relation formalism with the aim to improve predictions for the two-photon exchange corrections to elastic electron-proton scattering observables at finite momentum transfers. We study the formalism on the elastic contribution, and make a detailed comparison with existing data for unpolarized cross sections as well as polarization transfer observables.

Bohr Hamiltonian with Hulthén plus ring-shaped potential for triaxial nuclei

Abstract: In this paper, we solve the eigenvalues and eigenvectors problem with the Bohr collective Hamiltonian for triaxial nuclei. The β-part of the collective potential is taken to be equal to the Hulthen potential while the γ-part is defined by a new generalized potential obtained from a ring-shaped one. Analytical expressions for spectra and wave functions are derived by means of a recent version of the asymptotic iteration method and the usual approximations. The calculated energies and B(E2) transition rates are compared with experimental data and the available theoretical results in the literature.

Perspectives for photonuclear research at the Extreme Light Infrastructure - Nuclear Physics (ELI-NP) facility

Abstract: The perspectives for photonuclear experiments at the new Extreme Light Infrastructure - Nuclear Physics (ELI-NP) facility are discussed in view of the need to accumulate novel and more precise nuclear data. The parameters of the ELI-NP gamma beam system are presented. The emerging experimental program, which will be realized at ELI-NP, is presented. Examples of day-one experiments with the nuclear resonance fluorescence technique, photonuclear reaction measurements, photofission experiments and studies of nuclear collective excitation modes and competition between various decay channels are discussed. The advantages which ELI-NP provides for all these experiments compared to the existing facilities are discussed.

Radiative corrections beyond the ultra relativistic limit in unpolarized ep elastic and Møller scatterings for the PRad Experiment at Jefferson Laboratory

Abstract: The clear 7σ discrepancy between measurements of the proton charge radius from muonic hydrogen Lamb shifts and those from hydrogen Lamb shift and electron scattering lead to both intense theoretical and experimental efforts to understand and explain this difference. In this regard, a new experiment (PRad) based on unpolarized ep elastic scattering cross section measurements normalized to Moller scattering is underway at Jefferson Laboratory to extract the proton charge radius based on new proton electric form factor down to values of momentum transfer squared Q 2, as low as 10−4 GeV/c)2. To reach the precision of the experiment in such a small Q 2 region requires reliable knowledge of radiative corrections. In this paper, we present a complete calculation of radiative corrections for unpolarized elastic ep and Moller scatterings performed within a covariant formalism resulting in the set of explicit formulas beyond the ultra relativistic approximation (m 2 ≪ Q 2), and numerical results for the kinematics of the PRad experiment.

f1(1285) decays into a0(980)π0, f0(980)π0 and isospin breaking

Abstract: We evaluate the decay width for the processes f 1(1285) → π0 a 0(980) and f 1(1285) → π0 f 1(980)taking into account that all three resonances are dynamically generated from the meson-meson interaction, the f 1(1285) from $$K^* \bar K - c.c.$$ and the a 0(980), f 0(980) from πη, $$K\bar K$$ and ππ, $$K\bar K$$ , respectively. We use a triangular mechanism similar to that of η(1405) → ππη, which provides a decay width for f 1(1285) → π0 a 0(980) with a branching fraction of the order of 30%, in agreement with experiment. At the same time we evaluate the decay width for the isospin-forbidden f 1(1285) → π 0 f 0(980), which appears when we consider different masses for the charged and neutral kaons, and show that it is much more suppressed than in the η(1405) → ππη case, but gives rise to a narrow shape of the π + π − distribution similar to the one found in the η(1405) → ππη decay.

Spallation reactions: A successful interplay between modeling and applications

Abstract: The spallation reactions are a type of nuclear reaction which occur in space by interaction of the cosmic rays with interstellar bodies. The first spallation reactions induced with an accelerator took place in 1947 at the Berkeley cyclotron (University of California) with 200MeV deuterons and 400MeV alpha beams. They highlighted the multiple emission of neutrons and charged particles and the production of a large number of residual nuclei far different from the target nuclei. In the same year, R. Serber described the reaction in two steps: a first and fast one with high-energy particle emission leading to an excited remnant nucleus, and a second one, much slower, the de-excitation of the remnant. In 2010 IAEA organized a workshop to present the results of the most widely used spallation codes within a benchmark of spallation models. If one of the goals was to understand the deficiencies, if any, in each code, one remarkable outcome points out the overall high-quality level of some models and so the great improvements achieved since Serber. Particle transport codes can then rely on such spallation models to treat the reactions between a light particle and an atomic nucleus with energies spanning from few tens of MeV up to some GeV. An overview of the spallation reactions modeling is presented in order to point out the incomparable contribution of models based on basic physics to numerous applications where such reactions occur. Validations or benchmarks, which are necessary steps in the improvement process, are also addressed, as well as the potential future domains of development. Spallation reactions modeling is a representative case of continuous studies aiming at understanding a reaction mechanism and which end up in a powerful tool.

Bayesian Monte Carlo method for nuclear data evaluation

Abstract: A Bayesian Monte Carlo method is outlined which allows a systematic evaluation of nuclear reactions using the nuclear model code TALYS and the experimental nuclear reaction database EXFOR. The method is applied to all nuclides at the same time. First, the global predictive power of TALYS is numerically assessed, which enables to set the prior space of nuclear model solutions. Next, the method gradually zooms in on particular experimental data per nuclide, until for each specific target nuclide its existing experimental data can be used for weighted Monte Carlo sampling. To connect to the various different schools of uncertainty propagation in applied nuclear science, the result will be either an EXFOR-weighted covariance matrix or a collection of random files, each accompanied by the EXFOR-based weight.

Comparative studies for different proximity potentials applied to α decay

Abstract: Half-lives of α decay of even-even nuclei calculated by using fourteen different versions of proximity potentials are compared to experimental data. The results show that the results of the generalized proximity potential 1977 are very much in agreement with the experimental data. In comparison with the distributions of nuclear potentials at small distances and the distributions of total potentials above the released energy Q α , it is found that at small distances the distributions of nuclear potentials have large difference and the distributions of total potentials are different among the listed proximity potentials. The different potential distributions affect the penetration probability of α, which is related to the half-life of the α decay for each nucleus. The generalized proximity potential 1977 is also used to calculate the half-lives of α decay of nuclei with odd mass numbers. The results show that the generalized proximity potential 1977 can calculate the half-lives of the α decay of almost all nuclei, which underlines and supports the use of the generalized proximity potential 1977 by Santhosh et al. in the Coulomb and proximity potential model (CPPM) and the Coulomb and proximity potential model for deformed nuclei (CPPMDN).

Multinucleon photonuclear reactions on 209 Bi: Experiment and evaluation

Abstract: Photon activation technique using bremsstrahlug with end-point energy 55.6 MeV is used to induce photonuclear reactions in a 209Bi target. Absolute yields and integrated cross sections of multiparticle reactions (γ, 2n-6n), (γ, 4n1p), and (γ, 5n1p) are obtained. The results are compared to predictions of statistical models using systematical and microscopic description of photoabsorption and to the result of evaluation of the partial photoneutron reaction cross sections. Based on a comparison with existing experimental photoneutron cross sections and model calculations, we make a conclusion that neutron multiplicity assignment in available photoneutron cross sections on 209Bi can be corrected and evaluated cross sections of (γ, 1n) and (γ, 2n) are obtained that are in an agreement with the obtained experimental results.

Non extensive thermodynamics and neutron star properties

Abstract: In the present work we apply non-extensive statistics to obtain equations of state suitable to describe stellar matter and verify its effects on microscopic and macroscopic quantities. Two snapshots of the star evolution are considered and the direct Urca process is investigated with two different parameter sets. q-values are chosen as 1.05 and 1.14. The equations of state are only slightly modified, but the effects are enough to produce stars with slightly higher maximum masses. The onsets of the constituents are more strongly affected and the internal stellar temperature decreases with the increase of the q-value, with consequences on the strangeness and cooling rates of the stars.

Branching ratios for the decay of d*(2380)

Abstract: Based on measurements, the branching ratios for the decay of the recently discovered dibaryon resonance $d^{*}(2380)$ into two-pion production channels and into the np channel are evaluated. Possibilities for a decay into the isoscalar single-pion channel are discussed. Finally, the electromagnetic decay of $d^{*}(2380)$ is considered.

The RIB production target for the SPES project

Abstract: Facilities making use of the Isotope Separator On-Line (ISOL) method for the production of Radioactive Ion Beams (RIB) attract interest because they can be used for nuclear structure and reaction studies, astrophysics research and interdisciplinary applications. The ISOL technique is based on the fast release of the nuclear reaction products from the chosen target material together with their ionization into short-lived nuclei beams. Within this context, the SPES (Selective Production of Exotic Species) facility is now under construction in Italy at INFN-LNL (Istituto Nazionale di Fisica Nucleare — Laboratori Nazionali di Legnaro). The SPES facility will produce RIBs mainly from n-rich isotopes obtained by a 40 MeV cyclotron proton beam (200 μA) directly impinging on a uranium carbide multi-foil fission target. The aim of this work is to describe and update, from a comprehensive point of view, the most important results obtained by the analysis of the on-line behavior of the SPES production target assembly. In particular an improved target configuration has been studied by comparing different codes and physics models: the thermal analyses and the isotope production are re-evaluated. Then some consequent radioprotection aspects, which are essential for the installation and operation of the facility, are presented.

First Measurement of the $\Sigma$ Beam Asymmetry in $\eta^{\prime}$ Photoproduction off the Proton near Threshold

Abstract: The $ \Sigma$ beam asymmetry in $ \eta^{\prime}$ photoproduction off the proton was measured at the GrAAL polarised photon beam with incoming photon energies of 1.461 and 1.480 GeV. For both energies the asymmetry as a function of the meson production angle shows a clear structure, more pronounced at the lowest one, with a change of sign around $ 90^{\circ}$ . The observed behaviour is compatible with P-wave D-wave (or S-wave F-wave) interference, the closer to threshold the stronger. The results are compared to the existing state-of-the-art calculations that fail to account for the data.

SU(4) symmetry of the dynamical QCD string and genesis of hadron spectra

Abstract: A large degeneracy of mesons of a given spin has recently been discovered upon reduction of the quasi-zero modes of the Dirac operator in a dynamical lattice simulation. Here it is shown that a symmetry group SU(4) ⊃ SU(2)L × SU(2)R × U (1)A ×C i is consistent with the observed degeneracy. It is argued that this symmetry group is a symmetry of the dynamical QCD string. Implications of this picture for a genesis of light hadron spectra are discussed.

High-statistics study of the reaction gamma p -> p 2 pi(0)

Abstract: The photoproduction of 2 pi(0) mesons off protons was studied with the Crystal Barrel/TAPS experiment at the electron accelerator ELSA. in Bonn. The energy of photons produced.in a radiator was tagged in the energy range from 600 MeV to 2.5 GeV. Differential and total cross sections and p pi(0)pi(0) Dalitz plots are presented. Part of the data was taken with a diamond radiator producing linearly polarized photons, and beam asymmetries were derived. Properties of nucleon and Delta resonances contributing to the p pi(0)7r final state were determined within the Bonn-Gatchina (BnGa) partial-wave analysis. The data presented here allow us to determine branching ratios of nucleon and Delta resonances for their decays into p pi(0)pi(0) via several intermediate states. Most prominent are decays proceeding via Delta(1232)pi, N(1440)1/2(+)pi, N(1520)3/2(-pi), N(1680)5/2(+)pi, but also p f (500), pf(0) (980), and pf(o)(1270) contribute to the reaction.

Resonance strengths in the 17,18 O(p, α) 14,15 N reactions and background suppression underground

Abstract: We report on measurements of resonance strengths and energies for the $ E_{p} = 151$ and 193 keV resonances in the 18O(p, $\alpha$ )15N and 17O(p, $\alpha$ )14N reactions, respectively, obtained during commissioning of a new setup for alpha-particle detection studies at the LUNA underground laboratory. Our values, $\omega\gamma (151)=164.2\pm 0.9_{stat} {}^{+12.1}_{-11.7} {}_{syst}$ meV and $\omega\gamma (193)=1.68\pm 0.03_{stat} \pm 0.12_{syst}$ meV, are in excellent agreement with those reported in the literature. New values of resonance energies are $ E_{p}=151.2 \pm 0.3$ keV and $ E_{p}=194.8 \pm 0.3$ keV, respectively, this latter with the highest precision to date. Comparative background measurements in silicon detectors overground and underground were also carried out, yielding up to a factor of 15 in background suppression at LUNA at energies around 200keV. This clearly demonstrates the usefulness of underground measurements in charged-particles experiments, especially at low detection energies.

A method to calculate fission-fragment yields Y(Z,N) versus proton and neutron number in the Brownian shape-motion model

Abstract: We propose a method to calculate the two-dimensional (2D) fission-fragment yield $Y(Z,N)$ versus both proton and neutron number, with inclusion of odd-even staggering effects in both variables. The approach is to use the Brownian shape-motion on a macroscopic-microscopic potential-energy surface which, for a particular compound system is calculated versus four shape variables: elongation (quadrupole moment Q2), neck d , left nascent fragment spheroidal deformation $ \epsilon_{f1}$ , right nascent fragment deformation $ \epsilon_{f2}$ and two asymmetry variables, namely proton and neutron numbers in each of the two fragments. The extension of previous models 1) introduces a method to calculate this generalized potential-energy function and 2) allows the correlated transfer of nucleon pairs in one step, in addition to sequential transfer. In the previous version the potential energy was calculated as a function of Z and N of the compound system and its shape, including the asymmetry of the shape. We outline here how to generalize the model from the “compound-system” model to a model where the emerging fragment proton and neutron numbers also enter, over and above the compound system composition.