1. On a Search for -Mesic Nuclei at MAMI-C
- N and A interaction
- -mesic nuclei
- signatures
- previous data
- new experiment at MAMI ?
V.L. Kashevarov, A.I. Lebedev, A.I. L’vov, L.N. Pavlyuchenko, G.A. Sokol (LPI)

2. N and A interaction
Experimental information on N interaction mostly comes from
N  N (and N  N)
in comparison with
N  N (and N  N).
Coupled-channel analysis
K is used for tuning (no direct data!)

3. Coupled-channel analysis by Green, Wycech. PR C 71, 014001(2005)
Though in literature there are Re aN from to fm and Im aN from to 0.49 fm.
Prominent feature of N interaction is excitation of the S11(1535) resonance near threshold.

5. Owing to Re aN > 0 there is an attraction between a slow 
Owing to Re aN > 0 there is an attraction between a slow  and nuclear matter.
First-order optical potential:
Actually the attraction is expected to be less due nucleon Fermi motion, broadening the S11(1535) resonance, and some other medium effects.
Dashed line: aN = i 0.22 fm Bhalerao, Liu, PRL 54, 865(1985) Dotted line: aN = i fm Green, Wycech, PRC 55, R2167(1997) Solid line: chiral unitary approach Inoue, Oset, NPA 710, 354(2002)

6. Effective N scattering length (Inoue, Oset)

7. -mesic nuclei
Bound states of  in nuclei Haider, Liu, PRC 34, 1845(1986)
Depending on the strength of the optical N potential such bound states exist at A>11 (Haider, Liu, 1986) or even at A=3 and 2 (Ueda, PRL 66, 297(1991)).
Large collisional width of  in medium due to N  N :
 =  v (NN) ~ 65 MeV at  = 0 .
Descreasing effects:
a) subthreshold energy [reduction of Im T(N  N)]
b) A overlap
H = K + V
- /2 = Im E = Im <  | H |  > = <  | Im V |  >
~ <  | (r) |  >

8. (local density)

9. (microscopic few-body calculation)

10. Reliable signature for -mesic nucleus: decay products.
Cf. near-threshold enhancements in  production
dp   3He (COSY-11, Smyrski et al. PL B649, 258 (2007))
tot = A (q / qbeam ) / | 1 – i a q | 2
not sentivite to the sign of the  3He scattering length a.
Exp: a =  (2.9  0.6)  i (3.2  0.4) fm.
Meanwhile, Re a > 0 = bound state
Im a < = no bound state.

11. Birth, Life, and Death of -mesic nuclei
Signature of the eta-mesic nucleus is a peak in the energy distribution of decay products (like N or NN) or in the energy transfer (E – EN1 ).
Both the quantities are measures of the energy of  in medium.
Spectral function for 12C vs the energy of  ( a rectangular-well optical potential)

12. Photoproduction of -mesic nuclei was considered by Lebedev, Tryasuchev (1989, 1991), Kohno, Tanabe (1989), Tryasuchev (1999, 2001).
Below some Lebedev’s and Tryasuchev’s results are quoted (mostly from Phys.Part.Nucl. 30, 606(1999); Phys.At.Nucl. 64, 346(2001))

14. Decays of -mesic nuclei (inferred from calculations of Chiang, Oset, Liu, PRC 44, 738(1991)):
~ 85% N through excitation and decay of S This mode with back-to-back pairs was suggested by Sokol, Tryasuchev (Sov.Phys.-Lebedev Inst. Reports, , 31(1991)) as a trigger in seaches for -mesic nuclei.
~ 15% NN through excitation of S11 and its two-nucleon decay in the nuclear matter
Isotopic content (for “heavy” nuclei):
N = 1/3 +n , 1/6 0p , 1/6 0n, 1/3 p
(due to isospin = ½)
NN = ~5% pp, ~5% nn, ~90% pn
(the latter is because the cross section of pn  pn (or d) near threshold is ~10 times bigger than the cross section of pp  pp)

15. pp  pp: – 1 =0
(but spins)
pn  pn: –1 – 2 = –3
Ratio ~ 1/9

16. (borrowed from Baru et al., PRC 67, 023002 (2003)

17. Previous photoproduction experiments (LPI and Mainz)
LPI: Sokol et al., Part. Phys. Lett. 102, 71 (2000); nucl-ex/
Bremsstrahlung photon beam up to 850 MeV of the LPI electron synchrotron. Time-of-flight spectrometry.

18. LPI 1-GeV electron synchrotron

19. LPI experimental setup

21. Mainz: Pfeiffer et al. PRL 92, 252001(2004)
Tagged photon beam up to 850 MeV of MAMI B. TAPS for detection and calorimetry of 0p.
(no p1 ) !!
Energy of the 3He nucleus = 4.4  4.2 MeV; width = 25.6  6.1 MeV

22. Possible experiment at MAMI / CB+TAPS
Suitable for pp and ppp
(what about ppn??)

23. Sample simulation Energy resolution of CB for 0 p  ~ 21 MeV
(for T = 300 MeV, Tp = 100 MeV)
Energy resolution of CB for p2 p3  ~ 23 MeV
(for Tp = 300 MeV)
Energy resolution of TAPS for p1  ~ MeV
(for Tp ~ 300 MeV, p ~ 10 – 15o )

24. Count rates

26. Conclusions Search for -mesic nuclei at MAMI in the reaction
 + A  p1 + (A-1), (A-1)  0 + p + X or p2 + p3 + X
seems feasible with the existing apparatus (Still further simulations are needed Backgrounds! ).
Time and energy resolutions of the setup as well as expected count rates are sufficient for obtaining valuable information on binding energies, widths, and branching ratios of light -mesic nuclei.
3He (?), 4He, 6Li, 9Be, 12C (or CH4), 14N, 16O (or H2O),… can be used as the target.