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Pairing correlation in atomic nuclei under extreme conditions
KTH, School of Engineering Sciences (SCI). (Nuclear Physics Group)ORCID iD: 0000-0001-9273-2513
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The pairing correlation has long been recognized as the dominant many-body correlation beyond the nuclear mean field. Pairing plays an essential role in many nuclear phenomena including the occurrence of a systematic odd-even staggering (OES) of the nuclear binding energy. Pairing interaction plays, in particular, a significant role in the stability of weakly bound nuclei. Therefore it has been one of the most critical topics in nuclear physics because of the weakly bound structure of all newly discovered nuclei. Beyond the line of stability, pairing interaction is not a residual interaction anymore. Its strength can be of the same order of magnitude as the mean field.  In this thesis we have focused on the pairing interaction in atomic nuclei under extreme conditions to investigate the structure of loosely bound nuclei near the dripline; to probe and globally assess different outcomes of various zero-range pairing interactions and their effect on the loosely bound low angular momentum states. How much can density-dependence in zero-range pairing interaction nuclei affect the line of stability? Calculations predict that pure density-dependent pairing interaction so-called surface interaction enhances the collectivity and gives stronger neutron pairing gap in nuclei far from stability, while, the density dependence pairing interaction does not affect the gap for bound nuclei as much. The odd-even staggering of nuclear binding energies has been investigated to estimate the empirical pairing gap. A 3-point formula Δ(3)C (1/2[B(N,Z)+B(N −2,Z)−2B(N −1,Z)]) is advocated in this thesis, which we believe it is more suitable to measure the magnitude of pairing gap in even-even nuclei. The strength of Δ(3)C can be a good indicator of the two-particle spatial correlation. One-quasiparticle energies and binding energy for those odd nuclei, which can be approximated by spherical symmetry, are calculated to obtain binding energy odd-even staggering (OES) in all known semi-magic even-even nuclei. The pairing strength is fitted globally to all available data on the OES of semi-magic nuclei with Z ≥ 8. The difference between different zero-range density-dependent pairing interactions reduces with this global fitted parameter. The difference between the mean pairing gap and the OES gets larger as we get closer to the dripline. At the end of the thesis, a simple model has been developed which shows that when the mean-field becomes shallower the odd-even staggering of charge radii is reduced.This thesis covers results that are not included in the three published papers and some complementary works on the subject.

Abstract [sv]

Parkopplingen i atomkärnan anses vara den dominerande mångkropparskorrelationen efter kärnmedelfältet. Parkoppling i atomkärnan spelar en viktig roll i många kärnfenomen,inklusive förekomsten av en systematisk udda-jämn förskjutning (OES) av bindningsenergin.Hos svagt bundna atomkärnor däremot spelar parkopplingen en signifikant roll för stabiliteten. Det gäller alla de nyupptäckta neutronrika atomkärnor som karakteriseras aven svag bindningsenergi där således parkopplingen blir ett kritiskt fenomen. När vi lämnar stabilitetslinjen och närmar oss linjen av spontan neutronsönderfall är parkopplingeninte längre obetydlig, utan tvärtom spelar en viktig roll för stabiliteten hos atomkärnan.Dess styrka kan vara av samma storleksordning som medelfältet. I denna avhandling har vi fokuserat på parkopplingen i atomkärnor under extrema villkor i syfte att undersöka strukturen hos löst bundna atomkärnor nära linjen för neutronsönderfall; att utforska och globalt bedöma resultaten av olika parkopplingar baserad på en deltakraft (räckvidd noll) och deras effekt på löst bundna tillstånd med lågt rörelsemängdsmoment. Hur mycket kan ett täthetsberoende i parkopplingen påverka stabilitetslinjen? Beräkningarna förutsäger att ren densitetsberoende växelverkan för parkoppling, så kallad ytväxelverkan, ökar kollektiviteten i atomkärnan och ger ett större pargap för neutroner i kärnor långt ifrån stabilitetslinjen,medan densitetsberoende parkoppling påverkar inte gapet för bundna kärnor i samma omfattning.Udda-jämn-spridning av bindningsenergier har undersökts för att hitta storleken på parkopplingens gap. En 3-punktsformel Δ(3)C (1/2[B(N,Z)+B(N −2,Z)−2B(N −1,Z)]) förespråkas i denna avhandling, som vi anser vara mera lämplig för att mäta storleken på pargapet i jämn-jämna kärnor. Storleken på Δ(3)C kan vara en bra indikator på rumskorrelationen mellan två nukleoner. En-kvasipartikelenergi för de udda kärnorna, som kan approximeras med sfärisk symmetri, beräknas för att erhålla udda-jämn spridning (OES) med avseende på bindningsenergin för alla kända semi-magiska jämn-jämna kärnor. Parkopplingsstyrkan är globalt anpassat med all tillgänglig data på OES vad gäller semi-magiska kärnor med Z ≥ 8. Skillnaden mellan olika täthetsberoende parkopplingar med vår växelverkan minskar med dessa globalt anpassade parametrar. Skillnaden mellan det teoretiska genomsnittliga parkopplingsgapet och OES blir större när vi kommer närmare tröskeln för atomkärnans stabilitet. I slutet av avhandlingen har en schematisk modell utvecklats som, genom attgöra medelfältet grundare, reducerar de udda-jämnt spridda laddningsradierna. Avhandlingen innehåller dessutom resultat som inte ingår i de tre publicerade artiklarna samt några kompletterande arbeten om ämnet.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2017. , 88 p.
Series
TRITA-FYS, ISSN 0280-316X ; 69
Series
Pairing correlation in atomic nuclei under extreme conditions, ISSN 0280-316X
National Category
Subatomic Physics
Research subject
Physics
Identifiers
URN: urn:nbn:se:kth:diva-217522ISBN: 978-91-7729-537-2 (print)OAI: oai:DiVA.org:kth-217522DiVA: diva2:1156741
Public defence
2017-11-24, FA32, AlbaNova Universitetscentrum, Roslagstullsbacken 21, Stockholm, 10:34 (English)
Opponent
Supervisors
Note

QC 20171114

Available from: 2017-11-14 Created: 2017-11-14 Last updated: 2017-11-14Bibliographically approved
List of papers
1. Empirical pairing gaps, shell effects, and di-neutron spatial correlation in neutron-rich nuclei
Open this publication in new window or tab >>Empirical pairing gaps, shell effects, and di-neutron spatial correlation in neutron-rich nuclei
2015 (English)In: Nuclear Physics A, ISSN 0375-9474, Vol. 940, 210-226 p.Article in journal (Refereed) Published
Abstract [en]

The empirical pairing gaps derived from four different odd-even mass staggering formulas are compared. By performing single-j shell and multi-shell seniority model calculations as well as by using the standard HFB approach with Skyrme force we show that the simplest three-point formula δC(3)(N)=12[B(N,Z)+B(N-2,Z)-2B(N-1,Z)] can provide a good measure of the neutron pairing gap in even-N nuclei. It removes to a large extent the contribution from the nuclear mean field as well as contributions from shell structure details. It is also less contaminated by the Wigner effect for nuclei around N=Z. We also show that the strength of δC(3)(N) can serve as a good indication of the two-particle spatial correlation in the nucleus of concern and that the weakening of δC(3)(N) in some neutron-rich nuclei indicates that the di-neutron correlation itself is weak in these nuclei.

Keyword
Di-neutron correlation, Empirical pairing gap, Odd-even staggering, Pairing correlation
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-170315 (URN)10.1016/j.nuclphysa.2015.04.010 (DOI)000356127500012 ()2-s2.0-84930001942 (Scopus ID)
Funder
Swedish Research Council, 621-2012-3805, 621-2013-4323
Note

QC 20150629

Available from: 2015-06-29 Created: 2015-06-29 Last updated: 2017-11-14Bibliographically approved
2. Density dependence of the pairing interaction and pairing correlation in unstable nuclei
Open this publication in new window or tab >>Density dependence of the pairing interaction and pairing correlation in unstable nuclei
2015 (English)In: Physical Review C. Nuclear Physics, ISSN 0556-2813, E-ISSN 1089-490X, Vol. 91, no 2, 024305Article in journal (Refereed) Published
Abstract [en]

This work aims at a global assessment of the effect of the density dependence of the zero-range pairing interaction. Systematic Skyrme-Hartree-Fock-Bogoliubov calculations with the volume, surface, and mixed pairing forces are carried out to study the pairing gaps in even-even nuclei over the whole nuclear chart. Calculations are also done in coordinate representation for unstable semimagic even-even nuclei. The calculated pairing gaps are compared with empirical values from four different odd-even staggering formulas. Calculations with the three pairing interactions are comparable for most nuclei close to the beta-stability line. However, the surface interaction calculations predict neutron pairing gaps in neutron-rich nuclei that are significantly stronger than those given by themixed and volume pairing. On the other hand, calculations with volume andmixed pairing forces show noticeable reduction of neutron pairing gaps in nuclei far from stability.

Place, publisher, year, edition, pages
American Physical Society, 2015
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-162961 (URN)10.1103/PhysRevC.91.024305 (DOI)000350174000001 ()2-s2.0-84922511228 (Scopus ID)
Funder
Swedish Research Council
Note

QC 20150331

Available from: 2015-03-31 Created: 2015-03-26 Last updated: 2017-11-14Bibliographically approved
3. Odd-even staggering in neutron drip line nuclei
Open this publication in new window or tab >>Odd-even staggering in neutron drip line nuclei
2016 (English)In: Nuclear Physics A, ISSN 0375-9474, E-ISSN 1873-1554, Vol. 951, 97-115 p.Article in journal (Refereed) Published
Abstract [en]

We have done systematic Hartree-Fock-Bogoliubov calculations in coordinate space on the one-quasi-particle energies and binding energy odd-even staggering (OES) in semi-magic nuclei with the zero-range volume, mixed and surface pairing forces in order to explore the influence of their density dependence. The odd-N isotopes are calculated within the blocking scheme. The strengths for the pairing forces are determined in two schemes by fitting locally to reproduce pairing gap in 120Sn and globally to all available data on the OES of semi-magic nuclei with Z≥8. In the former calculations, there is a noticeable difference between the neutron mean gaps in neutron-rich O, Ca, Ni and Sn isotopes calculated with the surface pairing and those with the mixed and volume pairing. The difference gets much smaller if the globally optimized pairing strengths are employed. The heavier Pb isotopes show the opposite trend. Moreover, large differences between the mean gap and the OES may be expected in both calculations when one goes towards the neutron drip line.

Place, publisher, year, edition, pages
Elsevier, 2016
Keyword
Density dependence, Hartree-Fock-Bogoliubov approach, Nuclear pairing, Odd-even staggering
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-186920 (URN)10.1016/j.nuclphysa.2016.03.056 (DOI)000376795100007 ()2-s2.0-84962448801 (Scopus ID)
Funder
Swedish Research Council, 621-2013-4323
Note

QC 20160518

Available from: 2016-05-18 Created: 2016-05-16 Last updated: 2017-11-14Bibliographically approved
4. Empirical residual neutron-proton interaction in odd-odd nuclei
Open this publication in new window or tab >>Empirical residual neutron-proton interaction in odd-odd nuclei
2016 (English)In: PHYSICAL REVIEW C, ISSN 2469-9985, Vol. 93, no 3, 034334Article in journal (Refereed) Published
Abstract [en]

Two types of average neutron-proton interaction formulas are compared: In the first type, neutron-proton interactions for even-even and odd-A nuclei extracted from experimental binding energies show a smooth behavior as a function of mass number A and are dominated by the contribution from the symmetry energy. Whereas in the second type large systematic staggering is seen between even-A and odd-A nuclei. This deviation is understood in terms of the additional neutron-proton interaction in odd-odd nuclei relative to the neighboring even-even and odd-A systems. We explore three possible ways to extract this additional interaction from the binding energy difference of neighboring nuclei. The extracted interactions are positive in nearly all cases and show weak dependence on the mass number. The empirical interactions are also compared with theoretical values extracted from recent nuclear mass models where large unexpected fluctuations are seen in certain nuclei. The reproduction of the residual neutron-proton interaction and the correction of those irregular fluctuations can be a good criterion for the refinement of those mass models.

Place, publisher, year, edition, pages
American Physical Society, 2016
National Category
Subatomic Physics
Identifiers
urn:nbn:se:kth:diva-185626 (URN)10.1103/PhysRevC.93.034334 (DOI)000373105400001 ()2-s2.0-84963682697 (Scopus ID)
Funder
Swedish Research Council, 621-2012-3805, 621-2013-4323
Note

QC 20160429

Available from: 2016-04-29 Created: 2016-04-25 Last updated: 2017-11-14Bibliographically approved

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