We are performing an experiment to determine the electron neutrino mass with the precision of a few eV by measuring the tritium beta decay energy distribution near the endpoint. Key features of the experiment are a 2 eV resolution electrostatic spectrometer and a high-activity frozen tritium source. It is important that the source have electronic wavefunctions which can be accurately calculated. These calculations can be precisely made for tritium and the HeT/sup +/ daughter ion and allow determination of branching fractions to 0.1% and energy of the excited states to 0.1 eV. We discuss the excited final molecular state calculations and describe the experimental apparatus. 2 references, 6 figures

Fackler, O.

Mugge, M.

Sticker, H.

White, R.M.

Woerner, R.

UNT Digital Library

UCRL- 92373 PREPRINT aotif'ZWaM-'y AN EXPERIMENT TO MEASURE THE ELECTRON NEUTRINO MASS USING A FROZEN TRITIUM SOURCE 0. Fackler* M. Mugge , H. Sticker*, R. M. White-, R. Woerner^ This paper was prepared for submittal to Telemark III Mini Conference on Neutrino Mass and Low Energy Weak Interactions Telemark, WI - October 25-27, 1984 March 1985 «^^N| &> * ' " r' s '#Jjj *iiLv O&LfciS B&£ft»rj& A&fcSUK ^ i i A . • . ^ . - ^ * a J M Sft^^^^g^^^e^raftAKj SEL " This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author. * Rockefeller University t Fermilab f Lawrence Livermore National Laboratory * . DISTRIBUTION OF THIS DOCUMENT IS UNLIMiftD DISCLAIMER This document was prepared as an accoun'. of work sponsored by an agency of the United States Government. Neither the United Stales Government nor the Universiij of California nor any of their employees, makes any warranty, express or implied, or assum s any legal liability or responsibility for the accuracy, completeness, or useful­ness of any information, apparatus product, or process disclosed, or represents thai its use would nol infringe privately owned rights. Reference herein lo any specific commercial products, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring bj the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state <ir reflect those of the United States Government or the University of California, and shall not be used f'u advertising or product endorsement purposes. U C R L - - 9 2 3 7 3 AN EXPERIMENT TO MEASURE THE ELECTRON NEUTRINO MASS USING A FROZEN TRITIUM SOURCE DE85 0 0 9 5 8 4 0. Feckler*, M. Mugge +, H. Sticker*, R. White*, R. Woerner* •Rockefeller University, New York, NY 10021 yFermilab, Batavia, IL 60510 c T s ^ S ^ ° ° ^Lawrence Livermore National Laboratory f s-b ? t s / Livermore, CA 94550 -< -r/ ? J ?• f ABSTRACT We are performing an experiment to determine the electron neutrino mass with the precision of a few eV by measuring the tritium beta decay energy distribution near the endpoint. Key features of the experiment are a 2 eV resolution electrostatic spectrometer and a high-activity fro?en tritium source. It is important that the source have electronic wavefunctions which can be accurately calculated. These calculations can be precisely made for tritium and the HeT + daughter ion and allow determina­tion of branching fractions to 0.1% and energy of the excited states to 0.1 eV. We discuss the excited final molecular state calculations and describe the experimental apparatus. The goal of our experiment is to measure the neutrino mass to better than 2 eV. If the neutrino mass is finite, the tritium beta decay energy distribution changes appreciably only within a few neutrino masses from the endpoint (see Figure l). For a zero neutrino mass, the fraction of decays within 2 eV of the endpoint is only 2.6 x 10"^-. This small fraction dictates a low-background high-resolution spectrometer with lerpe acceptance. After beta decay, the resulting atom or molecule can be left in one of many excited states. These excited states take energy from the emerging beta and give rise to a number of branches in the Kurie plot each with a different endpoint energy (see Figure 1). The sum of these branches rerults in the observed Kurie plot. A believable physics result emerges only if one knows the occupation fractions and energies of these final excited states and hence, the expected shape of the measured distribution. In addition, the spectrometer resolution function must be well understood. Long tails in this function can introduce a significant smearing in the tritium beta decay spectrum. Such effects greatly complicate the interpretation of the data. Finally, the emerging electrons undergo a dE/dx loss in the source itself. Ideally, a measurement of the dE/dx loss is made and a consistent neutrino mass is determined in sources of different thicknesses. fflSHRBtlTlOH. flP THIS D8CUMENT IS UNLIMITED F iq . 1 . A f i n i t e neutrino mass af fects the shane of the Kurie p lo t only w i th in a few m of the eDtipoint as shown by contrast ing F ig . la f o r zero neutrino mass and in F ig . lb f o r f i n i t e neutr ino mass niy. In addi t ion, the e f fec ts of three f i n a l states on the Kurie p lo t are shown. For most complex molecules or t r i t i u m binding processes, the f i n a l s ta te ef fects are not calculable w i th s u f f i c i e n t p rec is ion . However, molecular t r i t i u m (T?) at l i q u i d helium temperatures i s ideal because the low intem.ofecular binding energy (on the order o f 1/400 eV) means i t essen t i a l l y has the e lec t ron ic wavefunction o f the f ree T2 molecule. Two independent groups are performing the f i n a l s tate ca lcu la t ions f o r molecular t r i t i u m . Each group has a qu i te d i f fe ren t approach. N. Winter ' determines" the e lec t ron i c wavefunction from a complete conf igura t ion i n te rac t i on c a l c u l a t i o n . W. Kolos 2 and h is coworkers determine the e lec ­t ron i c wavefunctions by minimizing the energies using 100 to 200 term e l l i p t i c wavefunctions. Both groups determine the nuclear wavefunctions by solving Schroedingers equation f o r the po ten t ia l energy curve for each of these e lec t ron ic s ta tes . For the bound s ta tes , the nuclear wavefunctions are determined fo r each v i b r a ­t i ona l and rotat ional quantum s ta te . As w i l l be discussed below, the i n i t i a l state for the molecule can be accurately taken as the ground e lec t ron ic state and the ground nuclear motion s ta te . On the other hand there w i l l be a d i s t r i b u t i o n o f f i n a l states i n each degree o f freedom. - 2 -The lowest electronic states for the HeT + daughter ion as a function of the helium-tritium internuclear distance are plotted in Figure 2. The transition probabilities to each of these states are shown as a function of the HeT + internuclear separation in Figure 3. This figure shows that most of these states have the wrong electronic configuration to nave any appreciahle transition probability. With the initial 7g internuclear separation of 1.4 A. U., there are only five electronic states, including the ground state, which have sufficiently large transition probabilities to give rise to distinct branches i:o the Ki/rie plot. As is expected from the closeness of the Tp and thP HeT + ground state inter-nuclear separations, most of the probability occurs for a tran­sition to the Hel + ground state. The probability of finding the HeT + ion in the ground state after the decay is approximately 60% which is to be compared with 70* in the decay of an isolated tritium atom. Pll tXi i r f l i r f t W H I /•• l<*' H . I f t -i.». • i* 01) JL «•"»•> I I I I I I tdJU—1*J«M 1 t 4 t t itiitt-tiirm HHUTIU. J.I. ' •Ml Half I H I I I I M I I I I /is« tl t i l l m i ) I » J < J I imWtHTIVI IlHHTItf. I.V. The transition proba-/ig. 3. 'bilities states from the T2 state to the HeT + daughter ion states as a function of inter-nuclear separation. For an Fig. 2. The lowest 28 electronic states for the HeT + daughter ion as a function of the helium-tritium initial separation of 1.4 A.U., internuclear distance. only 5 states have significant probability. -3-Unlike the atom, however, the HeT + ion in its ground state has both vibrational and rotational degrees of freedom which can absorb energy from the decay beta. At the liauid helium tempera­ture of our source, only the lowest vibrational and rotational states are populated. However, after the decay, when one of the atoms has been given an impulse from the decay beta, most of the possible vibrational and rotational states will he populated. Fortunately, even near the endpoint of the beta decay spectrum where the maximum energy transfer to the nucleus can occur, the energy transferred to the nucleus is too small to dissociate the HeT + daughter ion an appreciable fraction nf the time. The He7 + is primarily excited to a high vibrational state when, near the endpoint of the beta decay distribution, the decay beta is emitted nearly aligned with the internuclear axis. Con­versely, the HeT + ion is left in a highly excited rotational state when the decay beta is emitted nearly perpendicular to the internuclear axis. ̂  This coupling between the beta decay and the vibrational and rotational states gives a high density of states near the top of the potential well (see Figure 4). The full width of this distribution is about 2 eV and the full width at half height is on the order of 1 eV. As a consequence of this small spread, the ground state branch in the Kurie plot is smeared by only an average of 1 eV. This additional spread is a small penalty to pay for the ease of using molecular rather than atomic tritium. I Hi PKmiMUillf IHMHIMIIKMt "T-T.MI Fig 4. Probability distribution of ending up in various states for the Her electronic ground state due to rotational and vibrational excitations. The full width at half height is about 1 eV. -4-Our source is actually so l id t r i t ium rather than a free molecule. Nevertheless, the t r i t i um molecular wavefunction in the frozen sol id is very close to the molecular wavefunction of the free molecule. We can understand this Qualitatively by noting that the t r i t ium melting temperature implies that the intermole-cular binding energy is very much less than the orbi ta l electron binding energy. Consequently, we can expect a very small perturbation on the molecular wavefunction because of intermole-cular binding forces. Quantitively, the electron probabil ity density halfway to the nearest molecular neighbor is approximately 3 x 10~4 of the maximum. This small electronic overlap gives rise to a negligible distort ion of the molecular wavefunction. The depth of the internuclear potential well i s approximately 1,600 times deeper than the intermolecular potential wel l . This difference in binding energies also indicates a very small per­turbation of the molecular wavefunction in the so l id . A theoretical calculation of the change in the Tj> electronic wavefunction resulting from the effects of binding t r i t ium in the crystal l a t t i ce was done by L. Stolarczyk, Warsaw (reported to us by H. Monkhorst, University of Florida). He symmetrically ortho­gonal ized the wavefunctions and found that the fractional change in the wavefunction, A\|j/\p, is approximately 0.07X. This small change is not surprising since the inductive forces which bind the t r i t ium molecules in the sol id are "typically one to two orders of magnitude smaller than the exchange forces which govern molecular binding. The experimental evidence for a very small change in the electronic wavefunction resulting from the binding in the sol id comes from Raman spectra in gaseous and sol id hydrogen. The vibrational energy levels are determined by the shape of the internuclear potential well and the shape of this well is determined by the electronic wavefunction. The typical measured sh i f t in the vibrational energy levels resulting from the binding in solid hydrogen is about l/?000 eV. Since this energy shi f t is very small compared with the typical vibrational energy level spacing of about 0.1 eV, th is is evidence for a vpry small per­turbation in the molecular wavefunctions resulting from the inter­molecular binding in the so l id . Furthermore, the molecular binding forces ere so weak that the rotational states are hardly perturbed and the molecules can rotate as though they were nearly free. Hence, we conclude that the uncertainty in the transit ion probabil i t ies due to intermolecular binding in the solid is less than 0 .1* and about 0.1 eV for the energy level uncertainties. The experimental apparatus is shown in Fiqure 5. I t is con­tained in a vacuum tank 0.9 m in diameter and 7 m long. The tank is passively shielded by 2 concentric magnetic shields giving a residual f i e l d less than 2 milligauss in the active region. The source is a l iquid helium cooled plate on which t r i t ium is frozen. Varying the amount of t r i t ium gas introduced allows Collimator Source Solid State Detector Gate Valve Id Shaping Electrodes Focussing Electrodes Cosmic Ray Veto Fig. 5. Schematic view of the apparatus. The source at the left rotates from its vertical position to a horizontal by dotted lines. position as shown source thickness variation from a few monolayers up to any thick­ness. Following the source, a variable-length collimater defines the angular acceptance of the electrons. The spectrometer con­sists of three equally spaced grid planes with field shaping electrodes around the axis. We measure the integral number of electrons whose energies are higher than the center grid potential. Electrons leaving the spectrometer pass through an electrostatic lens which focusses them onto a solid state detector. This detector simply counts the electrons but does have a 1 kev energy resolution which aids in rejectinq low enerqy electrons and photons. The experimental apparatus was tested in early fall by looking at the 7.3 keV electron conversion electrons from "Co jhi•= line has an intrinsic HWHM of 0.6 eV. Ou measurement of this line showed a HWHM of 2 eV. This measured di .ribuion is shown in Figure 6. The tail on the low energy side is due to the occurence of close-lying satellites of the conversion lines produced by accompanying shake-off excitations. In conclusion, we have discussed why fro?en tritium is an ideal source offering the highest activity per dE/dx of any material and offering fully calculable final state effects. These final state effects contribute less than 0.2 eV of uncertainty to the final possible determination of the neutrino mass. In addition, we have built a spectrometer with a measured resolution of better than 2 eV. As we complete the cryogenic components of the experiment, our Monte Carlo studies show that our frozen source and our apparatus will be able to determine the neutrino mass to better than 2 eV. -6-citmtnTim, ceuwTiic w n Fig. 6. Measured distribution of the 7.3 KeV conversion electrons from a ^Co source. This line has an in­trinsic HWHH of 0.6 eV. Our measurenent has a HV.'HH of 2 eV. Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48 and by Fermilab and Rockefeller University. REFERENCES 1) N. Winter, Lawrence Livermore National Lab., and 0. Fackler, to be published. ?) W. Kolos, B. Jeziorski, K. Szalewicz, H. Monkhorst, to be published. -7-

Experiment to measure the electron neutrino mass using a frozen tritium source

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Experiment to measure the electron neutrino mass using a frozen tritium source

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