The mass of the electron neutrino from electron capture in 163Ho

11 August 1994 PHYSICS LETTERS B

ELSEVIER

Physics Letters B 334 (1994) 229-233

The mass of the electron neutrino from electron capture in

163Ho

S. Yasumi a,1, H. Maezawa a, K. Shima b, y. Inagaki c,2, T. Mukoyama a, T. Mizogawa e, K. Sera e, S. Kishimoto a, M. Fujioka g, K. Ishii g, T. Omori h, G. Izawa ~, O. Kawakami J a Nattonal Laboratory for High Energy Phystcs, KEK, lbarakz 305, Japan b Umverstty ofTsukuba, Ibarakt 305, Japan c Tsukuba lnstttute of Scwnce and Technology, lbarakt 300, Japan Kyoto Umverstty, Kyoto 611, Japan e Nagaoka College of Technology, Nugata 940, Japan f lwate Medtcal Untverstty, lwate 020-10, Japan g Tohoku Umversity, Mtyagz 980-77, Japan h Shlzuoka Umverstty, Shlzuoka 422, Japan ' Utsunomtya Bunsel Jumor College, Tochtgt 320, Japan J Mttsubtsht Materials Corporation, Aktta 010, Japan

Received 26 Apnl 1994 Edxtor L Montanet

Abstract

Using an M X-ray spectrum from electron capture m 163H0together with M X-ray fluorescence spectra of the Dy atom, the partml decay constants of 163Ho,AM~ and AM, were measured. With AM~, AM~ and At (total decay constant) as three constraints, the mass of the electron neutrino, mvo, the Q-value, and log(ft) of the 163Hodecay were simultaneously determined. Results +oloo keV, andlog(ft) -Ao°a+°°3° obtained are m r e-110+35°eV, -11o Q-2.710_ooo5 i

There are three ways to measure the mass o f the electron neutrino; the first one [ 1-3 ] proposed by De R f j u l a which is essentially based on the three-body phase space in the radiatlve electron capture process, the second one [ 4 - 8 ] which utihzes the mve-dependence of the electron capture rate, and the third one which is related to the bound-state/3 - - d e c a y [9] firstly observed by a GSI group. Our method falls under the second category.

Permanent address' Telkyo University, 359 Ohtsuka, Hachlojl, Tokyo 192-03, Japan 2 Present address' Tokyo Kasel Universxty, 1-18-1 Kaga, Itabashl, Tokyo 173, Japan 0370-2693/94/$07 00 © 1994 Elsevier Science B V All rights reserved SSD10370-2693 (94)00691-Y

~ . ~ J _ O ~

I .

It is well known that the 163H0 nucleus decays to 163Dy with a Q-value of ~ 2.7 keV by the capture of orbital electrons from the M and higher shells only (namely the N and O shells). For each shell the nucleus captures an electron predominantly from the Sl/2 subshell and from the Pl/2 subshell with much less probability. In the case of M capture, M X-rays of the dysprosium atom from M l ( 3 sl/2) and M2(3 Pl/2) electron capture in 163Ho are emitted and the rest mass mv~ can be determined from the intensities o f these Xrays. The principle of our method [ 10-12] for measuring mvo is described as follows. First, the M X-rays from M-electron capture in 163Ho are measured. If Sp '63n°

230

S. Yasuml et al / Phystcs Letters B 334 (1994) 229-233

stands for the photon spectrum from 163H0, where the number of photons per atom per second is plotted as a function of the energy of photons, we have

1 d Sp(k) '63H°[SM,(k) "NM, + SM2(k)"NM2] No dt

+ o'2(E~,, +a~)"SM2 + (r3(EM, +at)"SM3 q-O'4(EM, "}-A1)"SM4

d = dt [SM,(k)"nM~ +SM2(k)'riM2]

=SMI(k)'

SE.,+,a, = c[o'1(EM, +A1)"SM,

+ crs(EM, +A1)"SMs] ,

(3)

and

dnMl dnM2 dt +SM2(k)" d--t--

SE.,_A, = C[ O'2(EM, -- At)" SM2

= AM, • SM,(k) + AM2' SM2(k) , (1) where SM,(k ) ( i = 1, 2) IS the M X-ray spectrum from a Dy atom in the case where there is one vacancy in the M,(i= 1, 2) subshell only; k is the energy of emitted photons; ArM,(i = 1, 2) is the number of vacancies produced in the M, subshell in the decay 163H0 EC 163Dy; riM,(t = 1, 2) -- NM,/No; No is the total number of 163H0 atoms in the 163Ho source; AM,(i = 1, 2) is the partial M, electron capture decay constant. Eq. ( 1 ) shows that when we reconstruct the Sp 163n° spectrum using the SM, and SM2 spectra, the coefficients of SM, and SM~ correspond to AM, and AM:, respectively. Next, the SM, and SM2 spectra of the dysprosium atom can be obtained using the following method from fluorescence spectrum measurements in the photoionizanon of the dysprosium atom with monochromatic photons. If Se denotes an M X-ray fluorescence spectrum from Dy atoms excited by monochromatic photons having an energy E, Se is represented by the following equation:

-t- O'3(EM, - - A l ) "SM3 -t- O'4(EM, --AI)"SM4 + O'5(EM, --A1).SMs ] ,

(4)

where c - N m and N xs normalized. Photoionization cross sections for the M, subshell, tr,(E), can be represented by the power law cr,(E) = a , E - ~'(i = 1..... 5). We assume that all/3, in this equation are equal to two 3. Then Eqs. (3) and (4) become S~M,+ A, =C O',(EM, +A1)"SM, + C(EM, "~ A 1 ) - 2 X [az'SM2"I-O~3"SM3-~Of4"SM,-~- Ot5"SMs] ,

(5)

and SeM,-A, = C(EM, --A1) -2 X [O/2" SM2"t- 0/3" SM3"t- O/4"SM4=t-Olf5"SMs] ,

(6)

5

SE(k) = N m

~., o ' , ( E ) ' S M , ( k )

respectively. We multiply Eq. (6) by [ (EM, -- A1 ) / (EM, +A1 )]2, then we have

i=1

( i = 1. . . . . 5)

(2)

where cr,(E) is the photolonization cross section for the M, subshell for an incident photon of energy E; N is the total number of incident photons having an energy E; m is the number of dysprosium atoms in a target per cm 2. SM, in Eqs. ( 1 ) and (2) comprise the Auger and Coster-Kronig transition probabilities and the X-ray transition probabilities. In order to determine the SM, spectrum, we take two energies, EM, + A~ and EM, - A1 where EM, stands for the binding energy of the M~ subshell and the energy A~ is assumed to be comparable with the level width of the M~ subshell. Then, Eq. (2) becomes

(EM, -- AIt2

.-77 lj SM,_A, = C(EM, + A l ) - 2 X { O1~2"SM2"t- of3" SM3-[- ot'4"SM4"]-O~5"SM5} •

(7)

Subtracting Eq. (7) from Eq. (5), we get 3 The power law-least squares fitting for partial photolomzatmn cross sectmns showed that the exponents/3, are distributed m the range 1 58-2 85 Taking account that the A, are comparatwely small, ~t can be esnmated that thxs approxlmatmn introduces a systematic error of less than 1 5%

S. Yasumtet al / PhystcsLettersB 334 (1994)229-233

231

10~

2

Ma,B /'~ 4p-3s / \ M 4d-3p

f6SHo

%EM2

× [c cr2(EM2 +A2) ] -1

(9)

l0s

10z

8 I0

I

t

I

I

I

L

t 60 240 Channel Number

80

320

Fig 1 Photonspectrumfrom the 163Hosource

2 SEM,+AI -- t EMI -- A 1

~EMI +A1)

"SE~,_,I,

=C O'I(EMI "[-A1)"SMI

Finally we have 2

SMI(k)=[SEMI+ZlI(k)--xEMI'-~I )

" SEMI--

A1

× [c O'I(EM, +A1) ] - I

(8)

Similarly, using two fluorescence spectrum measurements with monochromatic photons whose energies are EM~ + A2 and EM~ -- A2 where EM2 stands for the bindlng energy of the M2 subshell and the energy A2 is assumed to be comparable with the level width of the M2 subshell, we get "Vacuum ,r

~St(LO

I

~

Shts

Detector

"

l

"

~

Crystal[InSb)

~ ~ m p L e Photon Counter

Mylar

Undulotor Rodlohon from BL-2A of the 25 GeV Pholon Factory Storage Ring ut KEK

Monochmmntor

Holder

Fig. 2 Experimental setup of the fluorescence spectrum measurement of the dysprosmm atom

On the other hand, At (total decay constant) of 163H0 can be determined by measuring the production rate of 163Dy due to electron capture in t63Ho with isotopedilution mass spectrometry [ 13,14]. Using AM~, AM: and At, the three unknown quantities, mve, the Q-value, and the log (ft) value relevant to the decay of 163Ho, can be simultaneously determined using the formula of electron capture beta decay. The photon spectrum from a 163Ho source was measured in vacuum with a Si(Li) detector (ORTEC) having a Be window 0.3 mll thick (nominal), [8]. The production of 163Ho using the 164Dy(p, 2n) reaction and the preparation of the 163Ho source at Tohoku University are described in our previous paper [6]. The whole apparatus was shielded with 100 mm thick lead. The counting time was 28.89. Fig. 1 shows a photon spectrum from the t63Ho source. The total number of 163Ho atoms in the 163Ha source, No, was measured at the University of Tokyo with isotope-dilution mass spectrometry [14] to be No= (6.481 -t-0.012) × 1015 atoms. The experimental setup of the fluorescence spectrum measurement on the dysprosium atom [ 15] is shown in Fig. 2. Undulator radiations from the 2.5 GeV Photon Factory Storage Ring at KEK were monochromated by a double-reflection crystal (InSb) monochromator and directed onto a Dy target. The intensity of incident photon beams was measured with a photon counter which consisted of a proportional counter and a Beabsorber. The proportional counter was filled with Kr gas admixed with 10% iso-butane at about 380 Torr. The counter can absorb the total energy of incident photons in the energy range of the present experiment. Using this counter, we measured the total number of incident photons, N, for each fluorescence measurement. Fluorescence M X-rays emitted at 90 ° to the direction of the incident beam in a horizontal plane from dysprosium atoms excited with incident photons, were measured with the same Si(Li) detector as that was used for measuring the photon spectrum from the 163Ha source [8]. It should be noted that elastic scattering

232

S Yasurm et al / Physt: s Letters B 334 (1994) 229-233 Sat c " o"t (2 0701

$tt2 CMz°'2 (1 848)

10~

ray transitions from the outermost shells of the Dy atom, namely Ms N7 and M 4 N 6 [ 8 ] . Therefore we decided to reconstruct Sp '~3a° in an energy region higher than the energy of My by using integral counts 4. Then, the reconstruction by Eq. (1) corresponds to solving two simultaneous equations of two variables, AM, and AM2. T h u s , AM1 and AM2 w e r e determined, respectively, to be

Io' o~t05 102

10 1

0

80

160

240 80 Chonnel Number

160

240

Flg 3 S p e c t r a Of SM~(k)'cM"O-I(2.070) andSM2(k) c M~"o'2(1.848), where c M~ and c M~ stand for the normahzed constants for M, and M2, respectwely.

could be largely suppressed in the direction of the Si(Li) detector, because the undulator photon beam is almost completely polarized in this direction as is shown in Fig. 2. At first, we measured the M : e d g e and the ME-edge of the Dy atom by changing the energy of the incident photons. Based on these measurements, we decided to take the values of 2.070 keV and 2.020 keV for EM, + A 1 and EMI -- a l , and 1.848 keV and 1.826 keV for EM~ + A2 and EM2 -- A2, respectively. Fluorescence spectra of Dy for these incident photons were measured whose elastic parts were subtracted using the response functions measured by our group [ 16]. Using Eqs. (8) and (9), we obtained SM, "CM'' O'1(2.070)-spectra and SM2" c M2"0"2( 1.848)-spectra as shown in Fig. 3, where c M'' o'l (2.070) = 401.7 × 10 6 and c M2. 0-2(1.848) = 178.9 × 10 6. In the reconstruction of t h e S p '63H° spectrum using SM, and SM2, it seems to be safer not to use the M~,~ peak in Fig. 1 and Fig. 3, because this peak includes X00190 00185

AM, = (0.9846+0.0492) × 10 -12 S - 1 , AMz = (0.0850+0.0026) × 10 -12 s - l These results are in good agreement with the values obtained by our previous experiment within experimental uncertainties where the theoretical SM, and SM2 spectra modified by the experiment were used [ 8 ]. On the other hand, the half-life of the 163Ho nucleus was determmed by measuring the production rate of 163Dy due to electron capture in 163H0 with isotopedilution mass spectrometry at the University of Tokyo as mentioned previously. Our result [ 14] is

T1/2 = 4 5 6 9 + 2 7 yr or

At = (4.807___0.028) × 10 -12 s-1 , which is in excellent agreement with Batsden et al.'s value [ 13 ]. Using the values of AM,, AM2 and At as three constraints, mvo, the Q-value and the log(ft) value for the decay of 163Ho EG --* 163Dy, were determined from the formula of the electron capture rate for the G a m o w Teller allowed transition [ 17 ]. The exchange and overlap correction factors were calculated by one of the authors by the use of the Dirac-Fock wave functions [ 18]. The radial wave functions at the position of the Holmium nucleus were taken from Ref. [18]. The results thus obtained are 11¢~+350

roVe = 11o_110

00180]

a~ ^'a/)'t

I

o o11~!

eV,

+o 1oo

2.710_ooo5 keV,

log(ft) --- A a,~ +o '-t-.~'.J _ 0 030 001 •

0 0170 I 0 0165 0 t8

(68% CL)

0 19

0 20

0.21

0.22

0.25

Fig. 4 shows a part of these results on a AM,/At versus AM2/At diagram. Therefore we conclude that

>'~t / >'t Ftg 4 Results of rn~ and the Q-value shown on a AM,/A t versus AM2/ A:dmgram.

4 Since the 5p-3s peak overlapped the elastm peak, it could not be used Furthermore, it was not easy to single out the Me peak without a large uncertamty

s Yasumt et a l / P h y s w s Letters B 334 (1994) 229-233

mve<460 eV

(68% CL).

W e are g r a t e f u l to P r o f e s s o r A. M a s u d a for m e a s u r i n g the h a l f - l i f e o f 163Ho. O n e o f the a u t h o r s ( S . Y . ) w o u l d like to a p p r e c i a t e v a l u a b l e d i s c u s s i o n s w i t h Dr. A. Y a g i s h i t a o f K E K - P F . F i n a l l y , w e w o u l d like to e x p r e s s o u r s i n c e r e g r a t i t u d e to t h e P h o t o n F a c t o r y s t a f f for t h e i r k i n d s u p p o r t a n d h o s p i t a l i t y . T h i s w o r k w a s p e r f o r m e d u n d e r t h e a p p r o v a l o f the P h o t o n F a c t o r y A d v i s o r y C o m m i t t e e ( P r o p o s a l No. 9 1 - 2 7 2 ) .

[9] [ 10]

[ 11 ]

[ 12]

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