Neutrino-nucleus  : Measurements vs. calculations Petr Vogel, Caltech Oak Ridge, Aug , 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 /M p and  can be accurately evaluated. (see Vogel & Beacom, Phys. Rev. D60, (1999) and Kurylov, Ramsey-Musolf & Vogel, Phys.Rev.C67,035502(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 L 1A (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)L 1A, where the functions a(E), b(E) are known, and b(E)L 1A contributes ~`a few’ %.

Fixing the parameter L 1A There are several ways to do this. One can use reactor data ( e CC and NC), solar luminosity + helioseismology, SNO data, and tritum beta decay. Here is what you get: reactors: 3.6(5.5) fm 3 (Butler,Chen,Vogel) Helioseismology: 4.8(6.7) fm 3 (Brown,Butler,Guenther) SNO: 4.0(6.3) fm 3 (Chen,Heeger,Robertson) tritium  decay: 6.5(2.4) fm 3 (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%. This is very difficult.

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

A=12 triad Q   MeV Q  = MeV

Experiment and theory agree very well (this reaction can be used for calibration) Exp.results (in cm 2 ): (KARMEN e, 98, DAR) (LSND e, 01, DAR) (LSND , 02, DIF) (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 cm 2, see Engel et al, Phys. Rev. C54, 2740 (1996)

e + 12 C 12 N * + 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 cm 2 ): (LSND, 01) (LSND, 97) (KARMEN, 98) (E225, 92)

Evaluation of the  for inclusive 12 C  e,e - )N * with DAR spectrum This is dominated by negative parity multipoles, calculation becomes more difficult. Here is what various people get (in cm 2 ): Kolbe CRPA Singh local density app. Kolbe CRPA, frac. filling Hayes SM, 3h  extrapolated Volpe SM, 3h  Volpe QRPA The agreement between different calculations, and with the experiment, is less than perfect.

True challenge, inclusive 12 C(    )N * with DIF Exp: LSND 02, ( )x cm 2 Calc: 17.5 – 17.8 (Kolbe, CRPA, 99) (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. 40 Ar( e,e - ) 40 K *, and 40 Ar( e,e + ) 40 Cl * RPA

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

Reaction   e,e - ) 127 Xe bound states This was proposed by Haxton,88 as a radiochemical solar detection reaction, similar to 37 Cl. The cross section, unlike 37 Cl, was based only on difficult calculations. To calibrate it, an experiment with DAR spectrum was performed at LAMPF, giving  stat)  (syst))x cm 2 (Distel 02) Calculations, performed earlier (Engel 94) gave  2.1 (for g A =1.0) or 3.1 (for g A =1.26)  The agreement is good, but the experimental uncertainty is large, and the issue of g A 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 208 Pb (in cm 2 ) For DAR: Kolbe & Langanke, Suzuki & Sagawa, For FD: T=6 MeV 8 MeV 10 MeV Volpe 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 208 Pb calculated with SKIII (solid) and SkO+ (dashed) interactions, in fm 2. From Engel et al. 03

Conclusions: 1)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 12 C 12 N g.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)

(the smaller is rate is more correct)