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• W1840805912 abstract "THE PRESENT PAPER AIMS AT GIVING A UNIFIED DISCUSSION OF THE INFLUENCE OF COLLECTIVE MOTIONS ION NUCLEAR REACTIONS, WHERE BY COLLECTIVE MOTIONS WE SBALL UNDERSTAND ESSENTIALLY THE TYPE OF SURFACE DEFORMATION AND COUPLING PROPOSED BY A. BOHR2, A GUIDING PRINCIPLE IN THE PRESENT PAPER WILL BE THE ANALOGY DISCUSSED PREVIOUSLY BY THE AUTHOR4, BETWEEN THE EFFECT OF SCATTERING OF SUOND WABES BY SOAP BUBBLES. IN BOTH PROBLEMS THE SCATTERING IS INFLUENCED BY INTERIOR AND SURFACE EFFECTS WITH MANY POINTS OF RESEMBLANCE. THE GENERAL OUTLINE OF THE PAPER GOES AS FOLLOWS: IN SECTION II WE GIVE A BRIEF ABSTRACT OF NATURE COLLECTIVE MOTIONS AND THEIR INTERACTIONS WITH INCIDENT NUCLEONS. IN SECTION III WE DEAL WITH A PERTURBATION METHOD FOR THE INELASTIC SCATTERING OF NUCLEONS BY COLLETIVE MOTIONS, WHERE WE START AN INITIAL STATE IN WICH THE SCATTERING OF NUCLEONS BY COLLETIVE MOTIONS, WHERE WE START FROM AN INITIAL STATE IN WICH THE SCATTERING BY THE INTERIOR OF THE NUCLEUS IS ALREADY TEKEN INTO ACCOUNT. THE INELASTIC SCATTERING AMPLITUDE IS DETERMINED IN TERMS OF THE INITIAL WAVE FUNCTION A THE SURFACE OF THE NUCLEUS IN THE INCOMING AND OUTGOING CHANNELS. IN SECTION IV WE DISCUSS THE VALIDITY OF PERTUBATION APPROXIMATION WITH THE HELP OF THE EXPECTATION VALUE FOR THE PERTURBED WAVE FUNCTION OF THE ANGULAR MOMENTUM Lz OF THE NUCLEON.WE FIND THAT PERTUBATION METHOD FAILS AT RESONANCE ENERGIES INSIDE A CERTAIN RANGE. IN SECTION V WE TURN THEN TO WHAT WE COULD CALL A TAMM - DANCOFF APPROACH TO THE COLLECTIVE EFFECTS, IN WHICH WE LIMIT OURSELVES TO A DEFINITE NUMBER OF STATES ( THE SIMPLEST CASE BEING TWO STATES OF 0 AND 1 PHONON RESPECTIVELY) AND CARRY OUT A RIGOROUS ANALYSIS FOR THEM. WE OBTAIN THE SCATTERING, AND FIND THAT FOR THE FORMER CASE THE LOGARITHMIC DERIVATE AT THE SURFACE IS A SUM OF TWO PARTS, ONE DUE TO THE INTERIOR OF THE NUCLEUS AND ONE DUE TO COLLECTIVE EFFECTS. THE NET RESULT OF THE INTERFERENCE BETWEEN THESE TWO EFFECTS WILL BE BROADENING OFTHE ORDINARY RESONANCES. THESE RESULTS ARE IN GENERAL AGREEMENT WITH THOSE OF THE RESONANCE AS SHOWN INTABLE #3 AND CORRESPONDING DECREASE IN THE MAXIMUM OF THE RESONANCES. THESE RESULTS ARE IN GENERAL AGREEMENT WITH THOSE OF THE CLOUDY CRYSTAL BALL MODEL. THE VALIDATY OF THE TAMM- DANCOFF APPROXIMATION IS DISCUSSED AGAIN WITH THE HELP PF THE EXPETATION VALUE OF Lz. THE ANALYSIS CARRIED OUT IN THE PREVIOUS SECTIONS IS GIVEN IN TERMS OF THE PHONON EXCITATION OF THE NUCLEUS WHICH WOULD BE LIKELY ONLY FOR NUCLEI NEAR CLOSED SHELLS. IN SECTION VI WE CONSIDER THE CASE OF STRONGLY DEFORMED TERGET NUCLEI, WHERE ROTATIONAL EXCITATIONS ARE LIKELIEST, AND DISCUSS THE SCATTERING OF NUCLEONS BY THESE NUCLEI, BOTH IN THE PERTUBATION AND TAMM - DANCOFF APPROXIMATIONS. THE ANALYSIS CAN BE CARRIED OUT IN A FASHION THE SIMILAR TO THAT OF THE PREVIOUS SECTIONS, AND THE FINAL RESULTS ONLY SUBSTITUTE THE DEFORMATION PARAMETER ² FOR THE 5Ћ(4BC)-1/2 OF THE PHONON CASE. THE BROADENING OF THE RESONANCES IS CORRESPONDINGLY CHANGED AS SHOWN IN TABLE #5. IN ALL PREVIOUS SECTIONS APPROXIMATIONS OF ONE SORT OR ANOTHER WERE MADE, NOT ALWAYS IN JUSTIFIABLE FASHION. IT IS OF INTEREST, THEREFORE, TO SHOW THAT A PROCEDURE SOMEWHAT SIMILAR TO THE ONE USED IN THE DISCUSSION OF THE SCATTERING OF SOUND WAVES BY SOAP BUBBLES COULD GIVE RISE TO FORMALIMS IN FOCK SPACE10 THAT ALLOWS AN EXACT DESCRIPTION OF THE SCATTERING OF NUCLEONS BY SURFACE MOTIONS. THE RESULTS OF THIS ANALYSIS JUSTIFY FROM ANTHER VIEWPOINT THE GENERAL CHARACTERISTICS OF THE SCATTERING PROCESS OBTAINED WITH THE HELP OF A TAMM- DANCOFF APPROXIMATION. FINALLY IN SECTION VIII WE RECAPITULATE SOME OF THE MAIN CONCLUSIONS AND INDICATE POSSIBLE FURTHER DEVELOPMENTS." @default.
• W1840805912 created "2016-06-24" @default.
• W1840805912 creator A5011554787 @default.
• W1840805912 date "2009-05-10" @default.
• W1840805912 modified "2023-09-26" @default.
• W1840805912 title "Movimientos colectivos y las reacciones nucleares" @default.
• W1840805912 hasPublicationYear "2009" @default.
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