Abstract
This text is dedicated to the memory of Jacques Raynal. I recall some of the interactions I had with Jacques from 1975 up until his death. I first met Jacques as a young student at Saclay in the mid 1970s and from then on we collaborated frequently. Jacques initiated me into elastic and inelastic scattering calculations in the coupled channels formalism. Within this formalism we calculated the excitation of Giant Resonance by light- or heavy-ion projectiles. We collaborated on the Coulomb corrections implemented in ECIS and later we tested numerically the Incoming Wave Boundary Condition, which is an important assumption when calculating sub-Coulomb fusion cross sections. He was among the first to understand the origin of what we would call the 3- excitation hindrance and suggest solutions.
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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The article is a review article with not new data.]
Notes
(ECIS) “Equations Couplées Itérations Séquentielles” is a coupled-channels code using a sequential iteration method for solving the coupled differential equations.
For the collection of Jacques’ codes see: http://www.oecd-nea.org/tools/abstract/detail/nea-0850/.
Paul Bonche worked from 1972 to 2006 as a theorist in the Nuclear Theory Division (SPhT) of CEA-Saclay.
Henriette Mathieu-Faraggi was the Director of the Department of Nuclear Physics (DPhN) at Saclay from 1972 to 1978. At that time the DPhN consisted of several divisions, the DPhN/BE, the LNS, the MF the HE, the ALS .... She was also President of the Nuclear Physics Committee of the International Union of Pure and Applied Physics (IUPAP). At the end of her tenure at DPhN and until her death in 1985 she worked at Saturne conducting experiments on the study of the properties of giant resonances in nuclei.
This was Bernard Bonin’s thesis work. Bernard subsequently had a brilliant career at the CEA; he was Deputy Scientific Director of the Nuclear Energy Directorate.
Quantum mechanically the wave function is written as a superposition of ingoing and outgoing waves. The Incoming Wave Boundary Condition (IWBC) consist of imposing only ingoing waves.
A similar conclusion was drawn for sub-Coulomb barrier fusion induced by exotic nuclei in the CDCC scheme [10].
However, one has to keep in mind that coupling to the continuum may not be fully represented by a simple reduction of the depth of the entrance channel potential, since the real part of the Dynamical polarization potential (DPP) may not have the same radial shape as the folded one.
Conceptually, sub-barrier fusion CC calculations should use only generic optical potentials that do not necessarily reproduce elastic scattering data a priori. Coupled channels effects may modify elastic scattering data and the deduced elastic scattering potentials may indirectly contain coupled channels effects. When calculating CC sub-barrier fusion with potentials that reproduce elastic scattering the same couplings can be considered, unintentionally, more than once! Completely satisfactory calculations are those that simultaneously describe all the coupled channels as well as the elastic scattering a posteriori. In the case of our paper, couplings other than the breakup (simulated by the potential) did not modify the sub-barrier fusion calculations. It is this last point that gave us confidence in our conclusions.
I first met Nick Keeley in 2003. Since then we have developed a strong friendship and a common perception of priorities in physics, important problems to deal with, and others that are just a waste of time.
Ray Satchler, born in London, England in 1926, was an internationally influential and respected nuclear theorist. In the 1980s he published two major books - An Introduction to Nuclear Reactions and Direct Nuclear Reactions. The latter is the definitive book on the topic and is still frequently cited. In 1977, for his seminal work on the theory and applications of direct nuclear reactions, he was awarded the Tom W. Bonner Prize by the Division of Nuclear Physics of the American Physical Society and in 1989 he was awarded a prestigious Doctor of Science degree by Oxford University for particularly outstanding contributions to his field of research. He died in Seattle, Washington, on March 28, 2010. https://physicstoday.scitation.org/do/10.1063/pt.4.1886/full/.
....Thank you for your letter just arrived. I can suggest pp. 599 et seq. of my book “Direct Nuclear Reactions and the enclosed paper. Confusion often arises because people do not define their S.R. ! I think Pitthan in referring to the “proton” S R, needed for B(El), and concerning the operator \(Q_{p}\) (eq.(14.63), p.600), rather than the “I S” and “I V” operators \(Q_{0}\) and \(Q_{1}\) of (14.62), p. 599. Although there are linearly related, \(Q_{p}=1 / 2 (Q_{0}+Q_{1})\), etc., the sum rules concern the squares of their matrix elements . : There are interference terms. As an example of the complication this can lead to, I can suggest what Pitthan may mean. Suppose there is a state, which exhausts the “I S” SR, \(\sum ^0\) of (14.66). The contribution of this to the proton sum rule, is \((Z/ A)^{2}\)\(\sum ^0\), (if \(\varrho _{n}/ \varrho _{p}= N/ Z\) etc.), while the proton sum rule, (14.68), is \(\sum ^p=Z/ A \sum ^0\) This leaves the remainder \([Z/ A-(Z/ A)^{2}] \sum ^0\) as contribution to the \(\sum ^p\) from other states (which I suppose one might call “I V” !) But this is just \([N/ Zx(Z/ A)^{2}] \sum ^0\), or N/Zx contribution from the postulated I S state. I think this a confusing way to look at it! For example if we were postulate an “out-of-phase”, or I V , giant resonance which enhances the I V sum the \(\sum ^I, (= \sum ^0)\)....its contribution to the proton sum will also be \((Z/ A)^{2}\sum ^0\). Thus the two states do not exhaust the proton sum rule \(\sum ^P\): there is still a fraction \((N-Z)/ A\) of \(\sum ^P \) to be found elsewhere. I hope I have not succeeded in confusing you further......
Maïmonide - Averroès : Une correspondance rêvée by Ili Gorlizki (2004-04-22).
The most recent version of Ian Thompson’s code FRESCO, FRESCOX, now includes options for relativistic kinematics. However, as one of the referees of this paper pointed it out, ECIS is the only one that includes the possibility of solving directly the Dirac equation.
The transition probability B(EL\(\uparrow )\) can be obtained by many methods such as Coulomb excitation measurements, lifetime measurements and electron scattering. Coulomb excitation and (e, e\(^{\prime }\)) measurements are sensitive to the properties of charge deformation. On the contrary, light- and heavy-ion inelastic scattering is sensitive to both the mass and charge deformation in a ratio which depends on the incident energy, the charge product of the colliding nuclei and the multipolarity of the transition.
Andrea Camilleri, “ La première Enquête de Montalbano ”.
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Alamanos, N. Jacques Raynal: memories of a physicist. Eur. Phys. J. A 56, 212 (2020). https://doi.org/10.1140/epja/s10050-020-00219-4
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DOI: https://doi.org/10.1140/epja/s10050-020-00219-4