The above conservatively large systematic hypothesis. TIle quoted uncertainties will be soon uncertainty reflects the fact that we did not finish reduced as our analysis progresses. evaluating the corrections fully in the current analysis We are simultaneously recording a large set of at the time of this writing, a situation that will soon radiative decay events for the processes t e'v y change. This result is to be compared with 1he and pi-+eN v y. The former will be used to extract previous most accurate measurement of McFarlane the ratio FA/Fv of the axial and vector form factors, a et al. (Phys. Rev. D 1984): quantity of great and longstanding interest to low BR = (1.026 ± 0.039)'1 I 0 effective QCD theory. Both processes are as well as with the (SM) furthermore very sensitive to non- (V-A) admixtures in prediction (Particle Data Group - PDG 2000): the electroweak lagLangian, and thus can reveal BR = (I 038 - 1.041 )*1 0-s (90%C.L.) information on physics beyond the SM. We are currently analyzing these data and expect results soon. (1.005 - 1.008)* 1W') - excl. rad. corr. Tale 1 We see that even working result strongly confirms Current P1IBETA event sxpelilnentstatistics, compared with the the validity of the radiative corrections. Another world data set. interesting comparison is with the prediction based on Decay PIBETA World data set the most accurate evaluation of the CKM matrix n >60k 1.77k element V d based on the CVC hypothesis and ihce >60 1.77_ _ _ results of measurements of superallowed Fermi l'+a e+v >580 M 0.35 M nuclear decays (PDG 2000): A+ ev y >58 k 1.35 k

BR = ( 1.037 ± 0.002)*l l'x p + - e+v v y >500 k 8.5 k Thus our preliminary result is ih very good agreement with the predictions of the SM and the CVC [X] T.Kozlowsk, IPJ Annual Report 2000 p.3 9

2.3 -less Double Capture - Potential Tool to Determine the Majorana Neutrino by Z.Sujkowski, S Wycech

The rate of neutrino-less double electron capturc by the emission of an additional particle as the energy strongly depends on the neutrino mass. This provides carrier. The most obvious candidate is a single photon, c\ the most sensitive method as yet proposed to but it could also be two photons, a conversion electron° determine this quantity. At the same time, the mere or a more exotic particle like a majoron. In general, observation of the phenomenon suffices to verify the any such emission slows down the process _ Majorana of the . considerably. of the order of 10-4 or worse. However, Most present or planned projects to scarch for ilic there exist favourable situations for such a , in neutrino-less double concentrate on double which the retardation can be largely or even totally 1 emission. The experiments rcly on the calorimetric compensated. This is so because of the very different measurement of the of the two P[ , phase space dependence of the radiative decays, (the The sum of these energies is constant, equal to ihe rate is proportional to Q3, where Q is the available total . This provides a convenient decay energy), and also because of the transition rates experimental signature, permitting one to distinguish increasing quickly with the of the the process from the much more abundant 2vpp decay. emitter (the ZAdependence). Thus the parameter to In the latter case the energy is shared statistically optimize is Z6/Q between the electrons and the neutrinos and the Table I lists a selected sample of nucleides as electron energy sum spectrum is continuous. The potential sources of the OvECECy decays. The half- simple principle of the experiment is thus to ernbed helie lives quoted are obtained by analogy with those source in a large, 4n detector (or to build the detector calculated for Ovpp decays. The uncertainty of this out of the source material) and to search for a procedure is reflected in the one or two order of monoenergetic signal taking care to assure low magnitude errors assigned to the final values for random background conditions. decays to the ground and excited states, respectively. We suggest [11 yet another process as a potential These uncertainties can be reduced by about a factor tool to search for the neutrino-less : of two with a state-of-the-art calculation of the nuclear the neutrino-less double . In order to matrix elements, yet to be done. conserve energy, this process has to he accompanied 40 Annual Report 2001

Table 1 The relative enhancement factors, R,,, Z6/(AEC - BK - A,)', and expected half-lives.

abundance AER T1 2 (y) % keVRei (m, = I eV) 144 ~~~~~~~1783 10 10o29±1 6.Sm 3.07 222(2(st.) l0 10,2±2 1846 2x100 5xI o29 ±l 24 2 68Er 0.139 1 00(1 st.) 2x10 6 5x l0 : 180 W 0.12 145 4xl 05 3xl 0o2 5 8 '48W 012 52 (2'st.) l01 1024±2

There are several experimental advantages in increases with lowering the decay energy, decays to designing the search for photons due to radiative excited states become of primary interest. As a result, electron capture. Firstly, the source may be relatively we may obtain another unique signature of the 2ffect - thick and separate from the detector. Contrary to the the coincident gamma radiation deexciting these state. electrons, the photons leave the source material The coincidence rates have been estimated [2] for without energy degradation, only with some intensity a few sources of table 1. The experiments are viewed attenuation. Secondly, the emission of the as feasible. The cost estimates remain to be done. photon due to capture is followed by that of an X-ray. The KX ray energies in heavy elements are typically 50-70 keV. Thus they emerge [I] Z.Sujkowski and S.Wycech, Acta Phys. Pol. from relatively thick source layers and are easily B32(2002)471 detectable. This makes it possible to design a [2] Z.Sujkowski and S.Wycech, Proc. Conf., Formio, coincidence experiment and thus to reduce the random Italy, 2002 l *l * background by a large factor. Thirdly, since the rate PL0201 806

2.4 Fission Barriers with Deformation-Dependent Attenuation of Shell Corrections by L.Shvedov, J.Blocki, J.Wilczyfiski

We have calculated heights of fusion barriers using We have made an important improvement on the a macroscopic model, in which the of predictions by implementing shell the fissioning nucleus is expressed in the effects to so far purely macroscopic calculations. We configurational space of three variables defining the correct the potential energies at the equilibrium shape volume conserving shapes of the mononuclear and/or by shell energies taken from the Thomas-Fermi dinuclear system. The fission barriers have been ground-state mass tables of Myers and Swiate-ki. We calculated as heights of the saddle point in the assume that the shell-correction energies S are potential energy surface (for symmetric split of the attenuated by deformation as postulated in Ref.[41: 2 system), taken relative to the ground-state energy S,1i S(1 - 202) Xp(-0 corresponding to the equilibrium shape. The potential energy was calculated as a sum of the where I nuclear potential taken in the form of the Yukawa- 02 = FIr(00p)-Ro2l plus-exponential potential of Krappe, Nix and Sierk 472 [1], and the Coulomb potential taken for realistic charge distribution with surface diffusion [2]. The is a measure of departure from spherical shape. The same scheme of purely macroscopic calculations was constant a2 has been determined in Ref.[4] by fitting previously applied by Sierk [3] for somewhat ground-state of deformed nuclei. differently parametrized nuclear shapes. Our calculations show that the attenuation of shell . . due to deformation of the fissioning, nucleus is We have compared results of our predictions. of the ~effects strona. With a value of the damping parameter taken macroscopic fission barriers with those of Sierk [3] Cs. W and we have found nearly perfect agreement for a wide from Ref. [4], shell effects get almost completely range of atomic numbers of fissioning nuclei. This washed out at the saddle configuration. Consequently, rsl ha eosaeothe ththh fission barriers, calculated as the energy at the result has demonstrated that heights of the z * > . ~~~~~~~~~~saddlepoint (with damped shell effects) relati,,e to the macroscopic fission barriers are not sensitive to the saddletoin (with damedsll efecs r i the particular choicepartiular of shapesape hoiceof parameterisation.prametrisaton. o round-state energy,c directly depend on the magnitude of the shell-correction energy at the ground stale.