NUCLEI Mid-Term Review: Science

NUCLEI Mid-Term Review:

Science

Joe Carlson, LANL (project PI)

Rusty Lusk ANL (Math/CS co-Director)

Witek Nazarewicz, MSU (Physics co-Director)

Microscopic valence-space Shell Model Hamiltonian

G.R. Jansen et al., Phys. Rev. Lett. 113, 142502 (2014)

S.K. Bogner et al., Phys. Rev. Lett. 113, 142501 (2014)

Coupled Cluster Effective Interaction

(valence cluster expansion) In-medium SRG Effective Interaction

MBPT IM-SRG

NN+3N-ind IM-SRG

NN+3N-full Expt.

0 1 2 3 4 5 6 7 8

Energy (MeV)

0⁺ 2⁺

2⁺ 2⁺

0⁺ 0⁺

(2⁺) 2⁺

2⁺

(0⁺) 0⁺

0⁺ 4⁺

4⁺ (4⁺)

4⁺ 2⁺

0⁺

2⁺

0⁺ 3⁺

3⁺ 3⁺

3⁺

0⁺

22

O

N2LO _sat describes low-energy NN and Nuclei

Reference A. Ekström et al. arXiv:1502.04682

• Order-by-order optimization (here: NN and NNN in N2LO)

• Constrained by data on few-body systems and light nuclei

• Focus on low-momentum physics

Accomplishments

• ^N2LO

performs well for finite nuclei and nuclear matter

• Extrapolates well all the way to Ca

isotopes.

Objectives

0 1 2 3 4 5 6 7 8

r (fm) 0.00

0.02 0.04 0.06 0.08 0.10

½ch (fm¡3 )

¡ ½_W

40Ca (Th.)

48Ca (Th.)

¢ Ca (Th.) Expt.

0 1 2 3 4 5 6 7 r (fm)

−0.01 0.00 0.01 0.02

r2¢½ch (fm¡1)

Landscape of Two-Proton Radioactivity

Objectives

• Ground-state two-proton (2p) radioactivity, the simultaneous emission of two protons by a nucleus, is a rare decay mode found in isotopes of elements with even atomic numbers located beyond the proton- rich border of the nuclear landscape. So far, this exotic process has been experimentally observed in a few light and medium-mass nuclides with atomic number Z < 32.

• Using state-of-the-art nuclear density functional theory, we globally analyze 2p radioactivity and for the first time identify the candidates for this exotic decay in elements heavier than strontium.

1. We quantified the landscape of ground-state 2p radioactivity.

2. We predict that almost all elements between argon and lead have 2p-decaying isotopes. The upper end of the 2p- decay territory is determined by alpha decay.

3. We predict a few cases where the competition between 2p emission and alpha decay may be observed. The observation of these two distinct decay modes in the same nucleus would provide an excellent test of nuclear structure models and a deeper understanding of charged particle emission from atomic nuclei.

Accomplishments

spectroscopic 2p dripline

Reference: E. Olsen et al., Phys. Rev. Lett. 111, 139903 (2013)

MADNESS-HFB: adaptive multi-resolution 3D DFT solver

Impact Objectives

• Complex many-body systems, such as fissioning nuclei, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies.

• To describe such systems, we introduce an adaptive

pseudospectral method for solving self-consistent equations of nuclear density functional theory (DFT) in three

dimensions. The numerical method is based on the multi- resolution and harmonic analysis techniques with a multi- wavelet basis.

• Enables rigorous predictive modeling in complex physical systems.

• The application of state-of-the-art parallel

programming techniques include sophisticated object- oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node.

• Provides benchmark for future model developments.

• The new adaptive multi-resolution solver MADNESS-HFB is benchmarked against a two- dimensional coordinate-space solver based on the B-spline technique and a three-dimensional solver based on the harmonic-oscillator basis expansion.

• The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary

constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory.

• This paper has been chosen by the Editors of Physical Review C as Editors Suggestion.

Accomplishments

Pedagogical illustration of adaptive representations in MADNESS-HFB. (a) The modulus squared of the single-neutron wave function corresponding to the single-particle energy of

−5.214 MeV obtained in MADNESS-HF calculations for

110Mo, and (b) the corresponding spectral refinement structure.

Reference: J.C. Pei et al., Phys. Rev. C. 90, 024317 (2014)

MADNESS applications

Calculations of nuclear pasta (IU) using 700 wave functions in a (24 fm)

box. Future plans include the extension of the code to larger systems with >5,000 wave functions.

Reference: J.C. Pei et al., Phys. Rev. C. 90, 024317 (2014) C. Horowitz et al., to be published

0 2 4 6 8 10 12 14 16 18

x, y, z (fm)

0.02 0.04 0.06 0.08 0.10

y x

z

0 5 10 15

-7 -6 -5 -4 -3 -2 -1

log 10(r n)

x, y, z (fm) r n (fm-3 )

HFODD(1140) HFODD(1540) MADNESS y

x

z 110

Mo

Neutron density distribution for the triaxial exotic nucleus

Mo in

MADNESS-HF, HFODD(1140), and

HFODD(1540) along x-, y-, and z-axis.

Defects in Nuclear Pasta and Crust Cooling of Neutron Stars

Reference: C.J. Horowitz et al., Phys. Rev. Lett. 114, 031102 (2015)

Objectives

• Use large scale GPU computing to perform

detailed molecular dynamics (MD) simulations of large regions of the neutron star crust, including complex nuclear pasta phases, to determine a variety of transport properties.

• Newly discovered topological defects in nuclear pasta phases can impact radio and X-ray

observations of neutron stars.

• Popular articles in Space.com, Phys.org, and NewScientist

• MD simulations with up to 409,600 nucleons led to discovery of new long-lived topological defects that reduce electron mean free path and decrease both electrical and thermal conductivities of neutron star crust.

• This is found to change the crust cooling rate 3 to 10 years after the end of an accretion episode in a Low mass X-ray binary (LMXB) and could lead to magnetic field decay in isolated neutron stars.

• Code IUMD scales well to at least 512 GPUs, now being ported to more GPUs on TITAN.

Accomplishments

Topological defects

Impact

ISNET: Enhancing the interaction between nuclear experiment and theory through information and statistics

Reference: J Dobaczewski et al. J. Phys.G 41 074001 (2014) (JPG highlight of 2014) http://iopscience.iop.org/0954-3899/page/ISNET

JPG Focus Issue

Around 35 papers (many from NUCLEI, including nuclear structure, reactions, nuclear astrophysics, medium energy physics, statistical methods… and fission…)

“Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful” (E.P. Box)

Error estimates of theoretical models: a guide

UNEDF2 functional: the endpoint of Skyrme DFT

Reference: M. Kortelainen, Phys. Rev. C 89, 054314 (2014)

radii

masses OES FI s.p.e.

Impact Objectives

 Develop predictive nuclear density functional theory to compute properties of light to heavy nuclei to understand global properties of nuclei, nuclear fission, and the formation of elements in the universe.

 Use the advanced optimization framework POUNDERS and carefully selected nuclear data to produce the well-calibrated Skyrme-type nuclear energy density functional UNEDF2 that represents an effective nuclear interaction.

 Enable rigorous, data-driven, predictive modeling of nuclear structure, which will reduce uncertainties stemming from nuclear science inputs in:

• basic science research such as tests of fundamental symmetries and nuclear astrophysics

• stockpile science and reactor physics

 Provide benchmark and template for future developments of nuclear structure models

1. We have developed a general framework to solve the self-consistent equations of nuclear density functional theory.

2. We have shown that:

• to constrain nuclear density functional, and provide uncertainty quantification, different types of data are required;

• traditional Skyrme functionals are intrinsically limited.

3. We have used the POUNDERS optimization framework and fast solver HFBTHO, developed and published under UNEDF/NUCLEI SciDAC projects.

Accomplishments

Sensitivity of the UNEDF2 parameters of the Skyrme energy density to different data types: atomic masses (red), charge radii (white), odd-even mass differences (blue), fission isomer excitation energies (green), and single-particle energies (yellow). The 4 fission isomer excitation energies and 9 single-particle energies represent only about 10% of the experimental data used but have a major impact on the final parameters.

Energy density functional for nuclei and neutron stars

Reference: J. Erler et al., Phys. Rev. C (2013)

Left: The mass-radius relation for neutron stars obtained with the nuclear functional SV-min (with the uncertainty band) and the uncertainty limits for the new functional TOV-min constrained to neutron star data indicated by blue arrows . Right: The covariance ellipsoid for the neutron skin R_skin in ²⁰⁸Pb and the radius of a 1.4M_⊙ neutron star calculated using SV-min. The mean values are: R (1.4M_⊙ )=10.18 km and R_skin= 0.17 fm.

Objectives

• Recent observational data on neutron star masses and radii provide stringent constraints on the

equation of state of neutron rich matter. We use the state-of-the-art nuclear density functional theory, coupled with state-of-the-art computational tools, to develop a nuclear energy density functional that can be simultaneously applied to finite nuclei and neutron stars

• By employing the covariance analysis, we assess correlations between observables for finite nuclei and neutron stars

Accomplishments

1.We developed the new functional TOV-min, informed by neutron star data to better constrain isovector interactions. TOV-min yields results for nuclear bulk properties of the same quality as those obtained with the

established functionals.

2.We demonstrate that standard energy density functionals optimized to nuclear data do not carry information on the expected maximum neutron star mass.

3.The new functional is expected to yield more reliable predictions in the region of very neutron-rich heavy nuclei.

Information Content of New Measurements

Reference: J. McDonnell et al. Phys. Rev. Lett. (2015)

Accomplishments

• Developed a Bayesian

framework to quantify and propagate statistical

uncertainties of EDFs.

• Showed that new precise mass measurements do not impose sufficient constraints to lead to significant changes in the

current DFT models

Bivariate marginal estimates of the posterior distribution for the 12-dimensional DFT UNEDF

parameterization.

Fission in NUCLEI

Quality Input Quality Input

Numerical Techniques Numerical Techniques

Large-scale Simulations

Large-scale Simulations Dynamics Dynamics

Confrontation with experiment

Confrontation with experiment

Excitation energy dependence of fission

Reference: J. McDonnell et al. Phys. Rev. C 90, 021302(R) (2014)

Accomplishments

• Elucidate the roles of proton and neutron numbers and excitation energy in

determining symmetric and asymmetric- fission yields

• Showed that excitation energy weakly affects the fission pattern of the nuclei considered.

E^*=5 4 4 5

11 10 9 11

18 18 16 18

28 30 28 27

Spontaneous fission of superheavy elements

Reference: A. Staszczak et al., Phys. Rev. C 87, 024320 (2013)

Accomplishments

• Breaking axial symmetry and parity turns out to be crucial for a realistic estimate of collective action; it results in lowering SF lifetimes by more than 7 orders of magnitude in some cases.

• We predict two competing SF modes: reflection symmetric and reflection asymmetric.

• The shortest-lived SH isotopes decay by SF; they are expected to lie in a narrow “valley of SF death.”

Trans-actinides

Superheavy nuclei

“critical” zones - 6

- 8 - 4 - 2 0 2 4 6 8 1 0 1 2 1 4 1 6 1 8

Z = 1 1 2

1 1 2 1 1 4 1 1 0 1 0 6

1 0 6 1 0 8 1 0 4 1 0 2 1 0 0

9 8 N= 1 26

N= 1 25 N= 18 4

1 4 0 1 4 5 1 5 0 1 5 5 1 6 0 1 6 5 1 7 0 1 7 5 1 8 0 1 8 5

N e u t r o n n u m b e r Log T (s)SF

T h e o r y Spontaneous fission half-lives

Spontaneous fission half-lives Actinides

48Ca-induced reactions

Oganessian et al.

Spontaneous fission lifetimes from the least-action principle

Impact Objectives

• Advanced theoretical methods and high-performance

computers may finally unlock the secrets of nuclear fission, a fundamental nuclear decay that is of great relevance to society.

• Spontaneous fission is a magnificent example of a motion during which the nucleus evolves in a multidimensional space of complex shapes, going through regions that are forbidden by classical mechanics.

• Enables rigorous data-driven predictive modeling in complex physical systems.

• Develops a predictive framework to describe spontaneous fission of a heavy nucleus

• Employs a dynamic approach based on minimization of the action integral in many dimensions.

• Uses symmetry-free DFT solver HFBODD, optimized for performance under UNEDF/NUCLEI SciDAC projects.

Accomplishments

Reference: J.Sadhukhan et al., Phys. Rev. C 88, 064314 (2013);

Phys. Rev. C 90 061304(R)(2014)

• Spontaneous fission has been studied employing realistic collective mass.

• The minimum-action fission path is strongly impacted by nucleonic pairing. The dynamical coupling between shape and pairing degrees of freedom can lead to a dramatic departure from the static picture. The notion of fission barrier is very limited.

• Computations optimized code for Cray architectures (using MPI/OpenMP).

• This paper has been chosen by the Editors of Physical Review C for the "Kaleidoscope"

elongation

triaxialitypairing

0 . 5 1 . 0

1 . 5 2 . 0 2 . 5

3 . 0 3 . 5

4 . 5 4 . 0

5 . 0

3 . 5

5 . 5

6 . 0 3 . 0

2 . 5 6 . 5

2 . 0

1 . 5 7 . 0

1 . 0

4 . 5 4 . 5

7 . 5

0 . 5 4 . 0

4 . 0

4 0 6 0 8 0 1 0 0 0

4 8

1 2 d y n a m i c

Q 22(b)

Q _{2 0}( b )

s t a t i c

ground

state saddle pre-scission

Finite-amplitude method for collective modes

Reference: N. Hinohara et al., Phys. Rev. C 87, 064309 (2013);

arXiv:1501.06994 (2015)

Accomplishments

• We propose a new method to compute low-lying collective modes in deformed nuclei.

• We demonstrate that the complex-energy FAM-QRPA method reproduces low-lying collective states

obtained within the conventional matrix formulation of the QRPA theory (MQRPA).

• We derive the sum-rule expressions from the contour integration of the complex-energy FAM. The method is very efficient and well-adaptable to parallel

computing. The FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used.

Computing Beta Decay All Over the Nuclear Chart

Reference: J. Engel, ArXiv: nucl-th/1405.0254

Objectives

• Develop a fast method for computing beta-decay within nuclear DFT.

• Compute beta-decay rates of all even-even nuclei, especially exotic, deformed nuclei that are

unreachable in experimental facilities.

Accomplishments

• We developed the proton-neutron finite amplitude method (pnFAM), a version of the charge-changing QRPA that scales far better than the usual approach, allowing beta-decay surveys across the nuclear chart.

• We started to improve EDFs, adding new terms so that they better predict beta decay. Initial results are very promising.

Using the pnFAM, we can compute strength functions (a) and decay rates (b) by examining the linear response in the complex-energy plane of the nuclear mean field to a perturbing force that turns neutrons into protons (or vice versa).

Impact

• Crucial input for r-process simulations.

• Use of beta-decay and Gamow-Teller

resonance data to determine nuclear

energy density functionals.

Atomic Electric Dipole Moment searches

Reference: E. Olsen et al., to be published

Accomplishments

• Developed efficient DFT solver to search for nuclear parity-breaking intrinsic shapes

• Carried out systematic calculations using six EDFs

• General agreement between different models

Survey of nuclear parity doublets with the

code AxialHFB [JPCS 402, 012034 (2012)].

Current 0nbb predictions

“There is generally significant variation among different calculations of the nuclear matrix

elements for a given isotope. For consideration of future experiments and their projected

sensitivity it would be very desirable to reduce the uncertainty in these nuclear matrix

elements.” (Neutrinoless Double Beta Decay NSAC Report 2014)

0nbb: Advanced Shell Model Approach

• Reduce the uncertainties of the 0nbb nuclear matrix elements.

• We use an interactive shell model approach that has been proven to accurately describe the

correlations around the Fermi level. By increasing the single particle model space we attempt to more accurately describe the nuclear matrix elements for medium-heavy nuclei.

• The knowledge of 0nbb nuclear matrix elements is essential for the design of the double-beta decay experiments and to identify physics beyond the Standard Model.

• Shared-memory parallel programming techniques were employed to increase the efficiency of the shell model code

• Provides benchmark for ab-inito calculations.

Accomplishments

Reference: A. Neacsu, M. Horoi, Phys. Rev. C 91, 024309 (2015)

• Large-scale calculation of the 0nbb nuclear matrix element of

Xe.

• First realistic shell model calculations of the 0nbb nuclear matrix elements beyond

closure approximation.

• New alternative method of calculating the nuclear matrix elements using pair

transitions.

Impact

Objectives

Our 0nbb strategy

Ab-initio

Solve “g

–quenching problem”

• Construct shell model interactions and effective GT operator from coupled cluster or IMSRG calculations in sd-shell nuclei. Include two-body currents.

• Obtain two-body effective GT shell-model operators for use with nuclei throughout sd shell. This will allow us to determine how much of g_A renormalization is due to two-body currents, and how much to correlations outside the phenomenological shell model.

Apply same methods to 0nbb decay

• Construct effective double-beta operators as well. This procedure and g_A work will tell us whether 0nbb decay is quenched anywhere near as much as 2nbb decay.

• Scale up to pfg shell, ⁷⁶Ge, ⁸²Se, other shells for, e.g.,

136Xe

Apply other methods to closed-shell isotopes, e.g.,

48

Ca,

O

• Benchmark Quantum Monte Carlo, coupled cluster theory, and NCSM.

DFT

Add all collective DOFs to GCM

• Include pn pairing, pp and nn pairing, triaxial

deformation as coordinates. Preliminary indications are that this may be enough for good 0nbb results.

GCM probably best option in heavier systems; can compute all candidate nuclei plus some sd-shell isotopes.

Understand overlaps of initial and final states In QRPA

Second QRPA

• Will give more accurate description of low-lying GT strength.

All these methods work with controlled expansions of interactions

and operators. Comparing results in nuclei that can be treated with

more than one method will help quantify error.