Ab initio calculation of the potential bubble nucleus Si34

Duguet, Thomas; Somà, Vittorio; Lecluse, Simon; Barbieri, C.; Navrátil, P.

doi:10.1103/physrevc.95.034319

Title: Ab initio calculation of the potential bubble nucleus ${}^{34}{Si}$

Abstract

Background: The possibility that an unconventional depletion (referred to as a “bubble”) happens in the middle of the charge density distribution of certain nuclei due to a purely quantum mechanical effect has attracted theoretical and experimental attention in recent years. Based on a mean-field rationale, a correlation between the occurrence of such a semibubble and an anomalously weak splitting between low angular-momentum spin-orbit partners has been further conjectured. Energy density functional and valence-space shell model calculations have been performed to identify and characterize the best candidates, among which ${}^{34}{Si}$ appears as a particularly interesting case. While the experimental determination of the charge density distribution of the unstable ${}^{34}{Si}$ is currently out of reach, ($d, p$) experiments on this nucleus have been performed recently to test the correlation between the presence of a bubble and an anomalously weak 1/2^––3/2^– splitting in the spectrum of ${}^{35}{Si}$ as compared to ${}^{37}S$ . Purpose: We study the potential bubble structure of ${}^{34}{Si}$ on the basis of the state-of-the-art ab initio self-consistent Green's function many-body method. Methods: We perform the first ab initio calculations of ${}^{34}{Si}$ and ${}^{36}S$ . In addition to binding energies, the first observables of interest are the charge density distribution and the charge root-mean-square radius for which experimental data exist in ${}^{36}S$ . The next observable of interest is the low-lying spectroscopy of ${}^{35}{Si}$ and ${}^{37}S$ obtained from ($d, p$) experiments along with the spectroscopy of ${}^{33}{Al}$ and ${}^{35}P$ obtained from knock-out experiments. The interpretation in terms of the evolution of the underlying shell structure is also provided. The study is repeated using several chiral effective field theory Hamiltonians as a way to test the robustness of the results with respect to input internucleon interactions. The convergence of the results with respect to the truncation of the many-body expansion, i.e., with respect to the many-body correlations included in the calculation, is studied in detail. We eventually compare our predictions to state-of-the-art multireference energy density functional and shell model calculations. Results: The prediction regarding the (non)existence of the bubble structure in ${}^{34}{Si}$ varies significantly with the nuclear Hamiltonian used. Yet, demanding that the experimental charge density distribution and the root-mean-square radius of ${}^{36}S$ be well reproduced, along with ${}^{34}{Si}$ and ${}^{36}S$ binding energies, only leaves the NNLO sat Hamiltonian as a serious candidate to perform this prediction. In this context, a bubble structure, whose fingerprint should be visible in an electron scattering experiment of ${}^{34}{Si}$ , is predicted. Furthermore, a clear correlation is established between the occurrence of the bubble structure and the weakening of the 1/2^––3/2^– splitting in the spectrum of ${}^{35}{Si}$ as compared to ${}^{37}S$ . Conclusions: The occurrence of a bubble structure in the charge distribution of ${}^{34}{Si}$ is convincingly established on the basis of state-of-the-art ab initio calculations. This prediction will have to be reexamined in the future when improved chiral nuclear Hamiltonians are constructed. On the experimental side, present results act as a strong motivation to measure the charge density distribution of ${}^{34}{Si}$ in future electron scattering experiments on unstable nuclei. In the meantime, it is of interest to perform one-neutron removal on ${}^{34}{Si}$ and ${}^{36}S$ in order to further test our theoretical spectral strength distributions over a wide energy range.

Authors:

Duguet, Thomas ^[1]; Somà, Vittorio ^[2]; Lecluse, Simon ^[3]; Barbieri, C. ^[4]; Navrátil, P. ^[5]

Univ. Paris-Saclay, Gif-sur-Yvette (France); Katholieke Univ. Leuven, Heverlee (Belgium). Inst. voor Kern- en Stralingsfysica; Michigan State Univ., East Lansing, MI (United States). Dept. of Physics and Astronomy
Univ. Paris-Saclay, Gif-sur-Yvette (France)
Katholieke Univ. Leuven, Heverlee (Belgium). Inst. voor Kern- en Stralingsfysica
Univ. of Surrey, Guildford (United Kingdom). Dept. of Physics
TRIUMF, Vancouver, BC (Canada)

Publication Date:: Thu Mar 23 00:00:00 EDT 2017

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1565610

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. C

Additional Journal Information:: Journal Volume: 95; Journal Issue: 3; Journal ID: ISSN 2469-9985

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Duguet, Thomas, Somà, Vittorio, Lecluse, Simon, Barbieri, C., and Navrátil, P. Ab initio calculation of the potential bubble nucleus Si34.  United States: N. p., 2017. 
Web.  doi:10.1103/physrevc.95.034319.

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                    Duguet, Thomas, Somà, Vittorio, Lecluse, Simon, Barbieri, C., & Navrátil, P. Ab initio calculation of the potential bubble nucleus Si34.  United States.  https://doi.org/10.1103/physrevc.95.034319

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                    Duguet, Thomas, Somà, Vittorio, Lecluse, Simon, Barbieri, C., and Navrátil, P. Thu .  
"Ab initio calculation of the potential bubble nucleus Si34".  United States.  https://doi.org/10.1103/physrevc.95.034319.  https://www.osti.gov/servlets/purl/1565610.

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@article{osti_1565610,

  title        = {Ab initio calculation of the potential bubble nucleus Si34},

  author       = {Duguet, Thomas and Somà, Vittorio and Lecluse, Simon and Barbieri, C. and Navrátil, P.},

  abstractNote = {Background: The possibility that an unconventional depletion (referred to as a “bubble”) happens in the middle of the charge density distribution of certain nuclei due to a purely quantum mechanical effect has attracted theoretical and experimental attention in recent years. Based on a mean-field rationale, a correlation between the occurrence of such a semibubble and an anomalously weak splitting between low angular-momentum spin-orbit partners has been further conjectured. Energy density functional and valence-space shell model calculations have been performed to identify and characterize the best candidates, among which Si34 appears as a particularly interesting case. While the experimental determination of the charge density distribution of the unstable Si34 is currently out of reach, ($d, p$) experiments on this nucleus have been performed recently to test the correlation between the presence of a bubble and an anomalously weak 1/2––3/2– splitting in the spectrum of Si35as compared to S37. Purpose: We study the potential bubble structure of Si34 on the basis of the state-of-the-art ab initio self-consistent Green's function many-body method. Methods: We perform the first ab initio calculations of Si34 and S36. In addition to binding energies, the first observables of interest are the charge density distribution and the charge root-mean-square radius for which experimental data exist in S36. The next observable of interest is the low-lying spectroscopy of Si35 and S37 obtained from ($d, p$) experiments along with the spectroscopy of Al33 and P35 obtained from knock-out experiments. The interpretation in terms of the evolution of the underlying shell structure is also provided. The study is repeated using several chiral effective field theory Hamiltonians as a way to test the robustness of the results with respect to input internucleon interactions. The convergence of the results with respect to the truncation of the many-body expansion, i.e., with respect to the many-body correlations included in the calculation, is studied in detail. We eventually compare our predictions to state-of-the-art multireference energy density functional and shell model calculations. Results: The prediction regarding the (non)existence of the bubble structure in Si34 varies significantly with the nuclear Hamiltonian used. Yet, demanding that the experimental charge density distribution and the root-mean-square radius of S36 be well reproduced, along with Si34 and S36 binding energies, only leaves the NNLO sat Hamiltonian as a serious candidate to perform this prediction. In this context, a bubble structure, whose fingerprint should be visible in an electron scattering experiment of Si34, is predicted. Furthermore, a clear correlation is established between the occurrence of the bubble structure and the weakening of the 1/2––3/2– splitting in the spectrum of Si35 as compared toS37. Conclusions: The occurrence of a bubble structure in the charge distribution of Si34 is convincingly established on the basis of state-of-the-art ab initio calculations. This prediction will have to be reexamined in the future when improved chiral nuclear Hamiltonians are constructed. On the experimental side, present results act as a strong motivation to measure the charge density distribution of Si34 in future electron scattering experiments on unstable nuclei. In the meantime, it is of interest to perform one-neutron removal on Si34 and S36 in order to further test our theoretical spectral strength distributions over a wide energy range.},

  doi          = {10.1103/physrevc.95.034319},

  journal      = {Physical Review. C},

  number       = 3,

  volume       = 95,

  place        = {United States},

  year         = {Thu Mar 23 00:00:00 EDT 2017},

  month        = {Thu Mar 23 00:00:00 EDT 2017}

}

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Title: Ab initio calculation of the potential bubble nucleus Si 34

Abstract

Citation Formats

Proton scattering by short lived sulfur isotopes journal, August 1999

Spin-orbit splitting in low- j neutron orbits and proton densities in the nuclear interior journal, February 2004

Shell structure of potassium isotopes deduced from their magnetic moments journal, September 2014

Status of the Nuclear Shell Model journal, December 1988

Nuclear magic numbers: New features far from stability journal, October 2008

Correlated density-dependent chiral forces for infinite-matter calculations within the Green's function approach journal, November 2014

Optimized Chiral Nucleon-Nucleon Interaction at Next-to-Next-to-Leading Order journal, May 2013

Medium-Mass Nuclei with Normal-Ordered Chiral N N + 3 N Interactions journal, July 2012

Solution of the Center-Of-Mass Problem in Nuclear Structure Calculations journal, August 2009

Renormalization of one-pion exchange and power counting journal, November 2005

Structure of Finite Nuclei in the Local-Density Approximation journal, April 1970

Ab initio self-consistent Gorkov-Green's function calculations of semimagic nuclei: Formalism at second order with a two-nucleon interaction journal, December 2011

Laser spectroscopy for nuclear structure physics journal, January 2016

Chiral three-nucleon forces and the evolution of correlations along the oxygen isotopic chain journal, July 2015

Nuclear “bubble” structure in Si 34 journal, March 2009

34Si: A new doubly magic nucleus? journal, September 1989

Experimental Study of the Two-Body Spin-Orbit Force in Nuclei journal, January 2014

New approach to the one-particle Green's function for finite Fermi systems journal, September 1983

Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory journal, October 2003

Local three-nucleon interaction from chiral effective field theory journal, November 2007

Relativistic corrections to the elastic electron scattering from Pb 208 journal, January 1976

New parametrization for the nuclear covariant energy density functional with a point-coupling interaction journal, November 2010

E FFECTIVE F IELD T HEORY FOR F EW -N UCLEON S YSTEMS journal, December 2002

Role of Long-Range Correlations in the Quenching of Spectroscopic Factors journal, November 2009

Table of experimental nuclear ground state charge radii: An update journal, January 2013

Translationally invariant density journal, July 2004

Charge distribution of the neven sulphur isotopes from elastic electron scattering journal, October 1983

Detecting bubbles in exotic nuclei journal, February 2008

CODATA recommended values of the fundamental physical constants: 2010 journal, November 2012

Does a proton “bubble” structure exist in the low-lying states of 34Si? journal, June 2013

Ab initio multireference in-medium similarity renormalization group calculations of even calcium and nickel isotopes journal, October 2014

Coupled-cluster calculations of nucleonic matter journal, January 2014

The mass of 35P and spin-parity assignments for excited 35P states journal, June 1985

Quadrupole Collectivity in 3 2 , 3 4 , 3 6 , 3 8 Si and the N = 20 Shell Closure journal, March 1998

Quasiparticle and quasihole states of nuclei around Ni 56 journal, June 2009

Beyond-mean-field study of the possible “bubble” structure of 34 Si journal, July 2012

Low-energy structure and anti-bubble effect of dynamical correlations in 46 Ar journal, January 2014

Nuclear axial current operators to fourth order in chiral effective field theory journal, March 2017

Modern theory of nuclear forces journal, December 2009

Isotopic Chains Around Oxygen from Evolved Chiral Two- and Three-Nucleon Interactions journal, August 2013

Nuclear charge densities with the Skyrme Hartree-Fock method journal, March 2003

Are occupation numbers observable? journal, April 2002

The size of the proton journal, July 2010

Chiral two- and three-nucleon forces along medium-mass isotope chains journal, June 2014

Radii and Binding Energies in Oxygen Isotopes: A Challenge for Nuclear Forces journal, July 2016

The ELISe experiment at FAIR journal, May 2007

First Demonstration of Electron Scattering Using a Novel Target Developed for Short-Lived Nuclei journal, March 2009

The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei journal, March 2016

Self-consistent Green's function method for nuclei and nuclear matter journal, April 2004

Structure of superheavy nuclei journal, March 2013

Weakly bound Borromean structures of the exotic 6,8He nuclei through direct reactions on proton journal, July 2015

Unveiling the Intruder Deformed 0 2 + State in Si 34 journal, August 2012

Nonobservable nature of the nuclear shell structure: Meaning, illustrations, and consequences journal, September 2015

High-precision quadrupole moment reveals significant intruder component in Al 20 13 33 ground state journal, September 2016

A 36S(d,p) study with high energy resolution journal, January 1989

A definition of the single-nucleon potential journal, June 1970

Spectroscopy of P 35 using the one-proton knockout reaction journal, March 2016

A proton density bubble in the doubly magic 34Si nucleus journal, October 2016

Accurate nuclear radii and binding energies from a chiral interaction journal, May 2015

The Ame2012 atomic mass evaluation journal, December 2012

Bubbles and semi-bubbles as a new kind of superheavy nuclei journal, March 2003

Unexpectedly large charge radii of neutron-rich calcium isotopes journal, February 2016

Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions journal, February 2016

Shell structure of superheavy nuclei in self-consistent mean-field models journal, August 1999

Ab initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei: Numerical implementation at second order with a two-nucleon interaction journal, February 2014

From low-momentum interactions to nuclear structure journal, July 2010

S 36 (d,p) S 37 and S 3 4 , 3 6 (d, He 3 ) P 3 3 , 3 5 reactions journal, November 1984

The size of the proton: From the Lamb-shift in muonic hydrogen journal, October 2011

The Ame2012 atomic mass evaluation journal, December 2012

Shell structure of superheavy nuclei in self-consistent mean-field models text, January 1999

CODATA Recommended Values of the Fundamental Physical Constants: 2010 journal, December 2012

Detecting bubbles in exotic nuclei text, January 2007

Local three-nucleon interaction from chiral effective field theory text, January 2007

Nuclear magic numbers: new features far from stability text, January 2008

Modern Theory of Nuclear Forces text, January 2008

From low-momentum interactions to nuclear structure text, January 2009

Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - I. Formalism at second order with a two-nucleon interaction text, January 2011

Title: Ab initio calculation of the potential bubble nucleus ${}^{34}{Si}$

Proton scattering by short lived sulfur isotopes
journal, August 1999

Spin-orbit splitting in low- $j$ neutron orbits and proton densities in the nuclear interior
journal, February 2004

Shell structure of potassium isotopes deduced from their magnetic moments
journal, September 2014

Status of the Nuclear Shell Model
journal, December 1988

Nuclear magic numbers: New features far from stability
journal, October 2008

Correlated density-dependent chiral forces for infinite-matter calculations within the Green's function approach
journal, November 2014

Optimized Chiral Nucleon-Nucleon Interaction at Next-to-Next-to-Leading Order
journal, May 2013

Medium-Mass Nuclei with Normal-Ordered Chiral $N N + 3 N$ Interactions
journal, July 2012

Solution of the Center-Of-Mass Problem in Nuclear Structure Calculations
journal, August 2009

Renormalization of one-pion exchange and power counting
journal, November 2005

Structure of Finite Nuclei in the Local-Density Approximation
journal, April 1970

Ab initio self-consistent Gorkov-Green's function calculations of semimagic nuclei: Formalism at second order with a two-nucleon interaction
journal, December 2011

Laser spectroscopy for nuclear structure physics
journal, January 2016

Chiral three-nucleon forces and the evolution of correlations along the oxygen isotopic chain
journal, July 2015

Nuclear “bubble” structure in ${}^{34}{Si}$
journal, March 2009

34Si: A new doubly magic nucleus?
journal, September 1989

Experimental Study of the Two-Body Spin-Orbit Force in Nuclei
journal, January 2014

New approach to the one-particle Green's function for finite Fermi systems
journal, September 1983

Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory
journal, October 2003

Local three-nucleon interaction from chiral effective field theory
journal, November 2007

Relativistic corrections to the elastic electron scattering from ${}^{208}{Pb}$
journal, January 1976

New parametrization for the nuclear covariant energy density functional with a point-coupling interaction
journal, November 2010

E FFECTIVE F IELD T HEORY FOR F EW -N UCLEON S YSTEMS
journal, December 2002

Role of Long-Range Correlations in the Quenching of Spectroscopic Factors
journal, November 2009

Table of experimental nuclear ground state charge radii: An update
journal, January 2013

Translationally invariant density
journal, July 2004

Charge distribution of the neven sulphur isotopes from elastic electron scattering
journal, October 1983

Detecting bubbles in exotic nuclei
journal, February 2008

CODATA recommended values of the fundamental physical constants: 2010
journal, November 2012

Does a proton “bubble” structure exist in the low-lying states of 34Si?
journal, June 2013

Ab initio multireference in-medium similarity renormalization group calculations of even calcium and nickel isotopes
journal, October 2014

Coupled-cluster calculations of nucleonic matter
journal, January 2014

The mass of 35P and spin-parity assignments for excited 35P states
journal, June 1985

Quadrupole Collectivity in $^{32, 34, 36, 38} Si$ and the $N = 20$ Shell Closure
journal, March 1998

Quasiparticle and quasihole states of nuclei around ${}^{56}{Ni}$
journal, June 2009

Beyond-mean-field study of the possible “bubble” structure of $^{34}$ Si
journal, July 2012

Low-energy structure and anti-bubble effect of dynamical correlations in $^{46}$ Ar
journal, January 2014

Nuclear axial current operators to fourth order in chiral effective field theory
journal, March 2017

Modern theory of nuclear forces
journal, December 2009

Isotopic Chains Around Oxygen from Evolved Chiral Two- and Three-Nucleon Interactions
journal, August 2013

Nuclear charge densities with the Skyrme Hartree-Fock method
journal, March 2003

Are occupation numbers observable?
journal, April 2002

The size of the proton
journal, July 2010

Chiral two- and three-nucleon forces along medium-mass isotope chains
journal, June 2014

Radii and Binding Energies in Oxygen Isotopes: A Challenge for Nuclear Forces
journal, July 2016

The ELISe experiment at FAIR
journal, May 2007

First Demonstration of Electron Scattering Using a Novel Target Developed for Short-Lived Nuclei
journal, March 2009

The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei
journal, March 2016

Self-consistent Green's function method for nuclei and nuclear matter
journal, April 2004

Structure of superheavy nuclei
journal, March 2013

Weakly bound Borromean structures of the exotic 6,8He nuclei through direct reactions on proton
journal, July 2015

Unveiling the Intruder Deformed $0_{2}^{+}$ State in ${}^{34}{Si}$
journal, August 2012

Nonobservable nature of the nuclear shell structure: Meaning, illustrations, and consequences
journal, September 2015

High-precision quadrupole moment reveals significant intruder component in ${}_{13}^{33}{Al}_{20}$ ground state
journal, September 2016

A 36S(d,p) study with high energy resolution
journal, January 1989

A definition of the single-nucleon potential
journal, June 1970

Spectroscopy of ${}^{35}P$ using the one-proton knockout reaction
journal, March 2016

A proton density bubble in the doubly magic 34Si nucleus
journal, October 2016

Accurate nuclear radii and binding energies from a chiral interaction
journal, May 2015

The Ame2012 atomic mass evaluation
journal, December 2012

Bubbles and semi-bubbles as a new kind of superheavy nuclei
journal, March 2003

Unexpectedly large charge radii of neutron-rich calcium isotopes
journal, February 2016

Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions
journal, February 2016

Shell structure of superheavy nuclei in self-consistent mean-field models
journal, August 1999

Ab initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei: Numerical implementation at second order with a two-nucleon interaction
journal, February 2014

From low-momentum interactions to nuclear structure
journal, July 2010

${}^{36}S$ (d,p) ${}^{37}S$ and ${}^{34, 36}S$ (d, ${}^{3}{He}$ ) ${}^{33, 35}P$ reactions
journal, November 1984

The size of the proton: From the Lamb-shift in muonic hydrogen
journal, October 2011

The Ame2012 atomic mass evaluation
journal, December 2012

Shell structure of superheavy nuclei in self-consistent mean-field models
text, January 1999

CODATA Recommended Values of the Fundamental Physical Constants: 2010
journal, December 2012

Detecting bubbles in exotic nuclei
text, January 2007

Local three-nucleon interaction from chiral effective field theory
text, January 2007

Nuclear magic numbers: new features far from stability
text, January 2008

Modern Theory of Nuclear Forces
text, January 2008

From low-momentum interactions to nuclear structure
text, January 2009

Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - I. Formalism at second order with a two-nucleon interaction
text, January 2011

Beyond-mean-field study of the possible "bubble" structure of 34Si
text, January 2012

Isotopic chains around oxygen from evolved chiral two- and three-nucleon interactions
text, January 2013