# Presentation: 785544

## Neutrino-nucleus :Measurements vs. calculations

- Petr Vogel, Caltech
- Oak Ridge, Aug. 28-29, 2003

***Outline:  a) review of known weak processes***
***                ******b) successes and difficulties***
***                ******c) unknown but important processes***
***                ******d) why we need to `calibrate’ nuclear***
***                     ******structure models***

- Note for the web etc. version:
- Throughout the selection of references is
- rather subjective and incomplete.
- Also, to save space, usually only the first author
- and year are given. Aficionados will easily
- recognize the correct reference.

- The simplest system – a single nucleon
- These two processes are governed by the same
- hadronic matrix element:
- n      p + e- + e   (neutron decay)
- e + p      n + e+   (inverse neutron decay)
- Knowing the neutron lifetime, 885.7(0.8), fixes the
- cross section for the relevant energies.
- The (relatively) small corrections of order E/Mp and 
- can be accurately evaluated.
- (see Vogel & Beacom, Phys. Rev. D**60**,053003 (1999) and
- Kurylov, Ramsey-Musolf & Vogel, Phys.Rev.C**67,**035502(2003))
- In this way the cross section of the inverse neutron decay can
- be evaluated with the accuracy of ~0.2%.

- A more complicated system – the deuteron
- There are many possible reactions now:
- e+ d         p + p + e- (CC)
- d        n + p +  (NC)
- the corresponding reactions with antineutrinos as well as
- p + p         d + e + e+  (pp in the Sun)
- p + p + e-         d + e (pep in the Sun)
- For all these reactions all unknown effects can be lumped
- together in one unknown parameter L1A (isovector two-body
- axial current) that must be fixed experimentally
- (_calibrating the Sun)._
- The cross section is of the form
- (E) = a(E) + b(E)L1A, where the functions  a(E), b(E) are
- known, and b(E)L1A contributes ~`a few’ % .

-              Fixing the parameter L1A
- There are several ways to do this. One can use reactor
- data (eCC and NC), solar luminosity + helioseismology,
- SNO data, and tritum beta decay. Here is what you get:
- reactors:                   3.6(5.5) fm3 (Butler,Chen,Vogel)
- Helioseismology:      4.8(6.7) fm3 (Brown,Butler,Guenther)
- SNO:                         4.0(6.3) fm3 (Chen,Heeger,Robertson)
- tritium decay:          6.5(2.4) fm3 (Schiavilla *et al.*)
- All these values are consistent, but have rather large
- uncertainties. To reduce them substantially, one would
- have to measure one of these cross sections to ~1%.

## Reaction e12C      12Ng.s.+ e-   

- This is an example of a process where the cross
- section can be evaluated with little uncertainty.
- We can use the known 12N and 12B  decay rate,
- as well as the exclusive capture on 12B and
- the *M1* formfactor for the excitation of the
- analog 1+, T=1 state at 15.11 MeV in 12C.
- This fixes the cross section value for (almost)
- all energies, for both e and .

## A=12 triad

- QMeV

- Q= 13.37 MeV

## Experiment and theory agree very well(this reaction can be used for calibration)

- Exp.results (in 10-42cm2):
- 9.4    0.4    0.8  (KARMEN e, 98, DAR)
- 8.9    0.3    0.9  (LSND e, 01, DAR)
-       8      10    (LSND , 02, DIF)
- 10.8     0.9    0.8  (KARMEN, NC, DAR )
- Calculations:  9.3 , 63, 10.5 (CRPA 96)
-                        8.8 , 60.4, 9.8 (shell model, 78)
-                        9.2 , 62.9, 9.9 (EPT , 88)

**Cross section for ****12****C(****************12****N****gs**** in 10****-42****cm****2****,**
**see Engel et al, Phys. Rev. C54, 2740 (1996) **

- e + 12C       12N* + e- (inclusive reaction)
- Here the final state is not fixed and not known,
- one cannot use (at least not simply as before)
- the known weak processes to fix the parameters
- of the nuclear models.
- The measurement is also more difficult since the
- experimental signature is less specific
- (units as before 10-42cm2):
- 4.3     0.4     0.6  (LSND, 01)
- 5.7     0.6     0.6  (LSND, 97)
- 5.1     0.6     0.5  (KARMEN, 98)
- 3.6     2.0             (*E225*, 92)

## Evaluation of the for inclusive12Ce,e-)N* with DAR spectrum 

- This is dominated by negative parity multipoles,
- calculation becomes more difficult. Here is what
- various people get (in 10-42cm2):
- Kolbe 95        5.9-6.3            CRPA
- Singh 98         6.5                 local density app.
- Kolbe 99         5.4-5.6           CRPA, frac. filling
- Hayes 00        3.8-4.1            SM, 3hextrapolated
- Volpe 00          8.3                 SM, 3h
- Volpe 00          9.1                 QRPA
- The agreement between different calculations, and with the
- experiment, is less than perfect.

## True challenge, inclusive12C()N* with DIF

- Exp: LSND 02, (10.6   0.3    1.8)x10-40cm2
- Calc:  17.5 – 17.8 (Kolbe, CRPA, 99)
-            16.6    1.4 (Singh, loc.den.app.,98)
-             15.2         (Volpe, SM, 00)
-              20.3         (Volpe, QRPA, 00)
-              13.8         (Hayes, SM, 00)
- Thus all calculations overestimate the cros section, with SM results noticeably smaller than CRPA or QRPA. The reason for that remains a mystery.

## But CRPA describes quite well electronscattering with similar momentum transfer

## Moreover, in another case (and a bit lower energies) CRPA (Kolbe) and SM (Haxton 87)agree quite well.

## CRPA angular distribution (which at low energy also agrees with SM)

## Let me now show some calculated forseveral cases of practical interest (ICARUS).These could be, therefore, used as both testsof calculations and basis for detector design etc.

- 40Ar(e,e-)40K*, and
- 40Ar(e,e+)40Cl* RPA

## CC cross section for e (T=4 MeV) on 52-60Fetotal  (full circles), n emission (empty), p (crosses)

## Reaction e,e-)127Xebound states

- This was proposed by Haxton,88 as a radiochemical
- solar  detection reaction, similar to 37Cl. The cross
- section, unlike 37Cl, was based only on difficult calculations.
- To calibrate it, an experiment with DAR
- spectrum was performed at LAMPF, giving
- *stat)**(syst))x10**-40**cm**2* (Distel 02)
- Calculations, performed earlier (Engel 94) gave
- 2.1 (for gA=1.0) or 3.1 (for gA=1.26)
- The agreement is good, but the experimental uncertainty
- is large, and the issue of gA renormalization remains
- unresolved.

## Charged current cross section on Pb

-   Lead based detectors are considered for SN detection.
- There are no experimental data, so the detector design
- has to rely on calculated cross sections.
-   Shell model treatment is impossible for such heavy nucleus,
- so various forms of RPA and other approximations are used.
-    The spread of the calculated values is often treated (for no
- logical reason, but nevertheless) as a measure of uncertainty
- of the calculated values.

## Calculated CC cross sections fore on 208Pb (in 10-40 cm2)

- For DAR:  Kolbe & Langanke, 01     36
-                  Suzuki & Sagawa, 03       32
- For FD:
-   T=6 MeV       8 MeV        10 MeV
-        14               25               35      Volpe 02
-        11               25               45      Kolbe 01
- Considerably larger were obtained by Fuller et al. 99;
- reasons for that overestimate are well understood, see
- Engel et al. 03 where the are close to Volpe 02

- CC  on 208Pb calculated with SKIII (solid)
- and SkO+ (dashed) interactions, in fm2.
- From Engel et al. 03

## Conclusions:

- Comparison between calculated and measured cross sections on complex
-      nuclei is sporadic or nonexistent.
-      _**Reliable and accurate data are needed**_
- 2) Different calculations agree on a ~30%
-      level for the energies relevant to SNS
-      or Supernovae. _** **_
- 3) However, if some (even small) number of
-      parameters could be adjusted (as for the
-      12C       12Ng.s.) a much better description
-      will likely result.

- Here are few slides I showed at the
- ORLAND workshop three years ago.
- They remain basically relevant for SNS2.

**(or SNS2)**

**(or SNS2)**

**(or SNS2)**

**(or SNS2)**

- (the smaller is rate
- is more correct)