# Presentation: 470351

## David J. Dean

***ORNL***

**                            ****Outline**
**Overview: general comments**
**Comments on nuclear structure**
**Neutrino interactions and the nucleus**
**Nuclear structure computation and neutrinos**
**The inverse reaction: electron capture**
**Conclusions**

**Nothing tends so much to the advancement of knowledge as the application of a new **
**instrument. The native intellectual powers of men in different times are not so much **
**the causes of the different success of their labors, as the peculiar nature of the means **
**and artificial resources in their possession.      -- *****Sir Humphrey Davy***

- Neutrino detection and nuclear structure research

## Nuclear structure landscapes

**Main goals:**
** ****Identify/investigate many-body **
**  ****methods that will extend to RIA**
** ****Generate effective interactions**
** ****Make reliable predictions**
** ****Guide experimental efforts**
** ****Pursue interdisciplinary overlaps**
**  ****(e.g., astro, weak interactions...)**
**Various approaches to  **
**low-energy nuclear theory:**
** ****Coupled-Cluster theory**
** ****Shell model Monte Carlo**
** ****DMRG/Factorization**
** ****Continuum shell models**
** ****Scalable parallel shell model**
** ****HFB**
** ****QRPA**
** ****TDHF**

## Physics issues

**What understanding do we gain from investigating the nuclear**
**many-body problem? **

**We will:**
** ****understand the evolution of the effective nucleon-nucleon interaction**
**       ****-- What is the isospin dependence?**
**       ****-- What is the density dependence? **
** ****understand foundations of independent particle motion**
**       ****-- How does shell structure change with increasing N?**
**       ****-- What is the role of the continuum in weakly bound nuclei?**
** ****understand excitation and decay properties of weakly bound systems**
**      ****-- Will neutron skins become clustered?**
**      ****-- What are the soft modes of excitation and core-skin correlations? **
** ****understand matter production in the universe**
**      ****-- What nuclear physics is important for understanding r-process nuclei? **
**      ****-- What is the role of nuclear science in SN explosion mechanisms?**

## Scientific triple point:

**Scientific triple point:**
**nuclear structure, nuclear astrophysics, weak interactions **

** ****Interplay of weak and strong forces**
**   ****plays a pivotal role in understanding **
**   ****astrophysics. **
** ****Astrophysics has become an important **
**   ****end-user of nuclear physics.**
** ****The three are intertwined. **

**We need information on:**
** ****masses**
** ****weak decay properties**
** ****neutrino interactions**
** ****thermal properties**

## Some Basics

**Some Basics**

**Charged current:**

**Neutral current:**

**All reactions are possible**
**as long as they obey selection rules**

## Why is 12C so ubiquitous?  Simplicity!

***Why is ******12******C so ubiquitous?  Simplicity!***

**Isospin **
**Triplet**

**Only the **
**isovector-axialvector **
**weak currents contribute **
**significantly to both reactions**

## Brief Formalism (from many papers)

**Brief Formalism ****(from many papers)**

**weak interaction**
**coupling constant**

**initial, final **
**nuclear energies**

**lepton momentum**
**and energy**

**neutrino energy**

**lepton traces +**
**nuclear matrix elements**

**One-body matrix**
**elements; known**

**Nuclear structure**
**information; needed**

**If the flux is known, the model dependence involved in **
**determining the one-body density matrix elements represents**
**the uncertainty of the predicted neutrino-nucleus cross sections. **

## Ab initio nuclear structure: Green Function Monte Carlo

**        ****(ANL/LANL/UIUC)**

**Since 1992:**
** ****algorithms**
** ****Variational MC**
** ****AV18 (2-body)**
** ****Computing**
** ****3-body interaction**

**For A=10, each state takes **
** ****1.5 Tflop-hours**

**Indicate the need for **
**3 (and 4?) body interactions**
**Future prospects:**
** ****A=12 by 2003/2004 (now)**
** ****triple alpha burning**
** ****Reaction aspects **
** ****NNN studies**

## Predicted neutrino cross sections (from ab initio theory): 12C

**Predicted neutrino cross sections (from ab initio theory): ****12****C**
**[Hayes, Navratil, Vary – PRL91, 12502 (2003)]**

** ****GFMC effort conclusively demonstrates the need for V****TNI**
** *****First***** calculation of neutrino-nucleus scattering in the shell model with V****NN**** + V****TNI**

## CD-Bonn

**AV8’+TM’**

| Interaction | 2hw | 4hw | 6hw | 4hw | Experiment |
| --- | --- | --- | --- | --- | --- |
| (e,e-) | 2.27 | 3.2 | 3.69 | 6.8 | 8.9+/-0.3+/-0.9 |
| (,-) | 0.168 | 0.275 | 0.312 | 0.537 | 0.56+/-0.08+/-0.1 |
| m-capture | 1.46 | 2.07 | 2.38 | 4.43 | 6.0+/-0.4 |

**Ab initio results for neutrino-nucleus (****12****C)**
**cross sections**

**V****TNI**** strongly affects the spin-orbit splitting in nuclei and **
**affects ****12****C****gs**** to the T=1,1****+**** states in mass 12. **

**Results are not completely converged**

## The role of RIA in determining drip-line properties

** ****RIA will probe the drip line to medium mass**
**   ****systems.**
** ****Shell structures will be far better understood. **
** ****Some of these systems exhibit large**
**   ****shape-coexistence phenomena, indicating **
**   ****complicated nuclear structure.**
** ****Why does one extra proton bind so many**
**  ****more neutrons?  **

***Saranzin et al., PRL84, 5062 (2000)***

**N=20 closure                           N=28 closure**

**What to measure for progress**
** ****masses (shell structure)**
** ****low-lying levels (shape coexistence)**
** ****Single particle states (shell structure)**
** ****decay widths (e.g., ****12****Be)**

## S2n (MeV)

**Evolution of shell structure**

** ****Do shell gaps disappear smoothly?  **
** ****Does the residual interaction affect **
**   ****the shell gap melting picture? **
** ****Continuum scattering acts to **
**   ****decrease  the shell gaps.**

***Dobaczewsk et al., PRC53, 2809 (1996)***

**Measurements:**
**   ****Masses (shell evolution)**
**   ****Decay properties (continuum)**
**   ****Low-lying spectroscopy**
**   ****Single particle state info**

## Mean-field calculations of separation energies

**Mean-field calculations of separation energies**

***RIA limit***

** ****Good overall agreement for measured systems**
** ****More masses will enable strong constraints on theory**

## HFB mass tables

**HFB mass tables**

**Stoitsov et al (submitted 2003); Goriely et al, PRC66, 024328 (2002)**

## Extensions of continuum shell-model approaches

**Extensions of continuum shell-model approaches**

** ****Widths of states depend on correct asymptotics. **
** ****Level repulsion may be important. **
** ****Continuum states affect bound states and visa versa**

**Michel et al PRL, 2003**

## Brief Formalism (from many papers)

**Brief Formalism ****(from many papers)**

**weak interaction**
**coupling constant**

**initial, final **
**nuclear energies**

**lepton momentum**
**and energy**

**neutrino energy**

**lepton traces +**
**nuclear matrix elements**

**One-body matrix**
**elements; known**

**Nuclear structure**
**information; needed**

**If the flux is known, the model dependence involved in **
**determining the one-body density matrix elements represents**
**the uncertainty of the predicted neutrino-nucleus cross sections. **

## Energy regimes and the SNS

** ****Low energy regime (< 10 MeV):**
**    ****Most important to provide a very detailed description of the nuclear wave **
**    ****function (via the shell model) for the initial and final states involved.**
** ****High energy regime (0.2 - 3 GeV):**
**    ****Relativistic Fermi gas + particle hole excitations.**
** ****Intermediate energy regime: 10 - 200 MeV**
**    ****Both the details of configuration mixing and particle-hole**
**    ****excitations play a significant role. Giant resonance regime**

**Energy regimes and the SNS**

**E****e**** > 40 MeV**

**E****e**** < 10 MeV**

**Nuclear excitation**
**ambiguous unless **
******’****s are measured**

**0 <E****nuc**** < 12 MeV**
**without measuring**
******’****s**

## Collective excitations induced by neutrinos: Resonances: ~20 MeV

**Radial excitations**

**Important property: cross sections**
**obey Thomas-Reiche-Kuhn **
**sum rule:**

***n***

***p***

***n***

***p***

***Typical E1***

***Spin-isospin GDR***

**Energy of GR’s scale like A****-1/3**

## Low energy regime: guidance from e-capture on nuclei

**Low energy regime: guidance from e-capture on nuclei**

***Koonin, Dean, Langanke, Phys. Rep. 278, 1 (1997)***
***Radha, Dean, Koonin, Langanke, Vogel, Phys. Rev. C56, 3079 (1997)***

## Systematic data in a given region of the periodic table

**Langanke, Martinez-Pinedo, Nucl. Phys. A673, 481 (2000)**

**Systematic data in a given region of the periodic table**

##  Model for electron capture on nuclei with N>40, Z<40. 

** ****Model for electron capture on nuclei with N>40, Z<40. **

**The science:**
** ****Electron capture on neutron-rich nuclei during the core collapse of a massive star. **
** ****In past supernova simulations, electron capture on nuclei is assumed blocked **
**   ****beyond the N=40 shell closure. **
**The model:**
** ****Use SMMC results for occupation probabilities at a given temperature (PP+QQ)**
** ****Include the occupation numbers as a starting point for RPA calculations.**

**Langanke, Kolbe, Dean, PRC63, 32801R (2001)**

## The role of nuclear structure in supernova

**The role of nuclear structure in supernova**

##   Needed e- Capture Rates

**Nuclei with A>120 are present during collapse of the core.**

**See: Langanke, Martinez-Pinedo, Nucl. Phys. A673, 481 (2000)**
**        ****Langanke, Kolbe, Dean, PRC63, 032801R (2001)**
**        ****Langanke et al (PRL, submitted, 2003) (rates calculation)**
**Hix et al (PRL, almost submitted) (core collapse implications)**

**Need experimental**
**BGT’s in fp-gds **
**shell nuclei. Experments**
**being planned at MSU**

## Nuclear physics impact: changes in supernova dynamics

**Nuclear physics impact: changes in supernova dynamics**

**e-capture on nuclei dominates**
**e-capture on protons**

**neutrino energies reduced**

**Reduces e-capture in outer region;**
**Increases e-capture in interior region **

**Shock forms deeper, but propagates **
**farther before stalling**

**Spherical; Newtonian**

## Nuclear structure impact on Supernova evolution 

**Neutrino-Nucleus scattering**

**Example:**
**Sampaio, Langanke, Martinez-Pinedo, Dean,**
**Phys. Lett. B529, 19 (2002). **
**-- cross section from shell model GT0 strength calculation. **
**-- low-energy neutrinos can upscatter from thermally **
**    ****excited states during collapse**
****** ****Increases neutrino energy, lowers entropy**

**Underway: systematic study in Z<40, N>40 systems (Juodagalvis) **

## Conclusions and Perspectives

-  **For a given nucleus measure (make a campaign):**
** ****Gamow-Teller strength distributions from np-reactions (SIBs)**
** ****e-A reaction cross sections in the lab (e.g., Darmstadt) **
** ****Use S(U4) to understand the expected ********-A response. **
** ****Make data cuts to obtain low-energy information**
-  **The quantum many-body problem requires significant effort. **
-    **Progress is being made, but ab inito theory is best done in light**
**   ****to medium-mass nuclei (new ideas may allow us to move to Fe). **
**   ****Models in heavier nuclei can be constrained by data, but**
**   ****these models often have less predictive power. **
-  **The future **
** ****Nuclear science requires measurements.**** **

## From applications to development:

**Coupled Cluster Theory**

**Some interesting features of CCM:**
** ****Fully microscopic**
** ****Size extensive: **
**  ****only linked diagrams enter **
** ****Size consistent: **
**   ****the energy of two non-interacting **
**   ****fragments computed separately is the same as that **
**   ****computed for both fragments simultaneously**
** ****Capable of systematic improvement**
** ****Not variational; in many cases behaves variationally**
** ****Amenable to parallel computing**

**Computational chemistry: 100’s of publications in 2002**
**(Science Citation Index) for applications and developments. **

## A short history

**Formal introduction:**
**1958: Coester, Nucl. Phys. 7, 421**
**1960: Coester and Kummel, Nucl. Phys. 17, 477**
**Introduction into Chemistry (late 60’s):**
**1971: Cizek and Paldus, Int. J. Quantum Chem. 5, 359**
**Numerical implementations**
**1978: Pople et al., Int. J. Quantum Chem Symp, 14, 545**
**1978: Bartlett and Purvis, Int. J. Quantum Chem 14, 561**
**Initial nuclear calculations (1970’s):**
**1978: Kummel, Luhrmann, Zabolitzky, Phys. Rep. 36, 1  and refs. therein**
**1980-90s: Bishop’s group. Coordinate space. **
**Few applications in nuclei, explodes in chemistry and molecular sciences****.**
** ****Hard-core interactions; computer power; unclear interactions**
**Nuclear physics reintroduction:**
**1999: Heisenberg and Mihiala, Phys. Rev. C59, 1440; PRL84, 1403 (2000)**
**	****   ****Three nuclei; JJ coupled scheme; bare interactions**
**Useful References**
**Crawford and Schaefer, Reviews in Computational Chemistry, 14, 336 (2000)**
**Bartlett, Ann. Rev. Phys. Chem. 32, 359 (1981)**

## Coupled Cluster Theory

**Correlated Ground-State**
**wave function**

**Correlation **
**operator**

**Reference Slater **
**determinant**

**Energy**

**Amplitude equations**

** ****With all T’s the spectrum of H is the **
**   ****same as the spectrum of the **
**   ****similarity transformed H; formally valid**
** ****In practice E closely approximates a**
**  ****variational theory when T is truncated**

**Work in progress with Morten Hjorth-Jensen**

## Choice of model space and the G-matrix

**Choice of model space and the G-matrix**

- Q-Space

- P-Space

**ph intermediate**
**states**

**We also include folded diagrams: eliminates or**
**reduces ********-dependence. **

## Tests of numerical convergence

**Numerical parameters:**
** ****Oscillator energy**
** ****G-starting energy**
** ****size of P space**

**Standard 1 body + 2 body Hamiltonians**
**derived from Chiral Lagrangians (EFT)**
**interactions supplied by R. Machleidt (Idaho).**
**(Also implemented CD-Bonn and others.)**

## Method of solution of CC equations

**nested commutators**
**(for H=H****1****+H****2****) for all T. **

**Method of solution of CC equations**

**Use Baker-Hausdorff**

**Normal order the Hamiltonian**

**Fock operator**

## T1 amplitudes from:

**Method of solution of equations**

- Note T2 amplitudes also come into the equation.

## T2 amplitudes from:

**T****2**** amplitudes from:**

**An interesting mess. **
**But solvable....**

**Nonlinear terms in t2**
**(4****th**** order)**

## On first iteration, assume that all t’s on the RHS of above

**equations are zero. Then:**

**Iterative Solution**

**Insert into the RHS and **
**obtain new amplitudes**
**Continue until **
**convergence**

## Correspondence with MBPT

## + all diagrams of this kind (11 more)  4th order

- + all diagrams of this kind (11 more)  4th order
- [replace t(2) and repeat above 3rd order calculation]

- + all diagrams of this kind (6 more) 4th order

**A few more diagrams**

## Ground states of helium and oxygen

**Ground states of helium and oxygen**

## Method			Energy (MeV)

**--------------------------------------------------------**
**CCSD****	****	****	****	****-23.607315**
**CR-CCSD[T],I****	****	****-24.4818**
**CR-CCSD[T],II****	****	****-24.5011**
**CR-CCSD[T(M3)],I****	****	****-25.362**
**CR-CCSD[T(M3)],II****	****	****-25.377**
**FULL CI****	****	****	****-24.92**

**Triples correction methods (w/ Piotr Piechuch, MSU)**
**He-4 (4 major oscillator shells) **