Neutrinoless Double <i>β</i><sup>+</sup>/EC Decays

<table>Values of the computed nuclear matrix elements for<svg height="18.549999" id="M435" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 40.474998 18.549999" width="40.474998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,13.884,14.05)"><path d="M509 373q0 -52 -42.5 -118.5t-124.5 -159.5l-94 -107h-27q-22 209 -78 342q-21 48 -41 48q-18 0 -63 -62l-22 21q77 111 125 111q30 0 52 -21.5t38 -75.5q37 -130 52 -285q48 62 74.5 99.5t53.5 87t27 76.5q0 43 -17 60q-5 5 -5 15q0 17 12.5 30.5t28.5 13.5
q21 0 36 -22.5t15 -52.5z" id="x1D708"></path></g><g transform="matrix(.017,-0,0,-.017,22.928,14.05)"><path d="M558 587q0 -32 -14 -61t-40 -53.5t-48.5 -41t-54.5 -36.5q144 -51 144 -174q0 -55 -43.5 -108t-104.5 -87q-77 -42 -131 -42q-31 0 -54 20t-31 47l11 18q48 -29 108 -29q79 0 119.5 43t40.5 109t-44.5 107.5t-119.5 50.5l22 47q34 1 65 21q96 61 96 157q0 42 -24 67.5
t-62 25.5q-24 0 -43.5 -9t-35 -29.5t-27 -44t-22.5 -63t-19.5 -75.5t-18.5 -91q-57 -294 -68 -380q-26 -190 -35 -200q-26 -31 -97 -37l-4 26q19 9 48 170l77 413q23 121 52.5 187.5t83.5 114.5q70 62 148 62q51 0 88.5 -34t37.5 -91z" id="x1D6FD"></path></g>
<g transform="matrix(.012,-0,0,-.012,32.812,5.887)"><path d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z" id="x2B"></path></g>
</svg>/EC decay transitions to the ground state (<svg height="21.25" id="M436" style="vertical-align:-5.73166pt" version="1.1" viewbox="0 0 18.8375 21.25" width="18.8375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,14.05)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.225,5.887)"><path d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z" id="x2B"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.225,18.137)"><path d="M463 437l5 -8q-21 -38 -45 -51l-57 3q30 -35 30 -88q0 -76 -52.5 -118t-122.5 -42q-24 0 -51 5q-30 -21 -30 -42q0 -16 16 -27t47 -11q19 0 54 0.5t52 0.5q36 0 65.5 -8t53.5 -36t24 -74q0 -77 -75 -137.5t-174 -60.5q-79 0 -126 37.5t-48 84.5q0 32 24 56q21 21 83 70
q-49 15 -74 55q-13 20 -11 42q56 21 88 61q-37 16 -62.5 51t-25.5 83q0 78 56.5 122t122.5 44h1q51 0 96 -27q71 4 136 15zM219 418q-34 0 -58 -32t-24 -87q0 -59 26.5 -96.5t67.5 -37.5q35 1 59 32t24 87q0 59 -26 96.5t-69 37.5zM241 -11q-62 0 -87 -21q-46 -39 -46 -78
q0 -41 38 -68.5t94 -27.5q69 0 106.5 31t37.5 80q0 52 -45 71q-33 13 -98 13z" id="x67"></path></g><g transform="matrix(.012,-0,0,-.012,13.794,18.137)"><path d="M319 325l-25 -7q-33 99 -103 99q-29 0 -47 -19.5t-18 -49.5t22 -49.5t62 -36.5q63 -26 95 -57t32 -79q0 -64 -50 -101t-115 -37q-35 0 -67.5 10.5t-46.5 23.5q-5 11 -11 51t-6 67l27 5q14 -53 46.5 -88.5t75.5 -35.5q29 0 50 19.5t21 50.5t-19.5 51.5t-59.5 39.5
q-28 12 -46 22.5t-38.5 27t-30.5 38.5t-10 49q0 54 42.5 92t109.5 38q48 0 88 -18q6 -15 13 -50.5t9 -55.5z" id="x73"></path></g>
</svg>), the first excited<svg height="14.3125" id="M437" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 27.225 14.3125" width="27.225" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,14.05)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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<g transform="matrix(.012,-0,0,-.012,13.888,5.887)"><path d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z" id="x2B"></path></g>
</svg>state (<svg height="18.200001" id="M438" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 15.8875 18.200001" width="15.8875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,14.05)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.225,5.887)"><path d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z" id="x2B"></path></g><g transform="matrix(.012,-0,0,-.012,8.225,18.138)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg>) and the resonant<svg height="14.3125" id="M439" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 27.225 14.3125" width="27.225" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,14.05)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.888,5.887)"><path d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z" id="x2B"></path></g>
</svg>state (<svg height="18.3375" id="M440" style="vertical-align:-3.39069pt" version="1.1" viewbox="0 0 22.5875 18.3375" width="22.5875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,14.05)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.225,5.887)"><path d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z" id="x2B"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.225,18.137)"><path d="M181 342h2q63 107 121 107q24 0 41 -16t17 -34q0 -34 -32 -49q-17 -7 -26 2q-21 20 -43 20q-20 0 -42 -22t-38 -63v-183q0 -50 12.5 -62t69.5 -16v-26h-230v26q47 5 58 17t11 61v207q0 49 -9 60.5t-53 16.5v23q74 12 141 40v-109z" id="x72"></path></g><g transform="matrix(.012,-0,0,-.012,12.485,18.137)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g><g transform="matrix(.012,-0,0,-.012,17.542,18.137)"><path d="M319 325l-25 -7q-33 99 -103 99q-29 0 -47 -19.5t-18 -49.5t22 -49.5t62 -36.5q63 -26 95 -57t32 -79q0 -64 -50 -101t-115 -37q-35 0 -67.5 10.5t-46.5 23.5q-5 11 -11 51t-6 67l27 5q14 -53 46.5 -88.5t75.5 -35.5q29 0 50 19.5t21 50.5t-19.5 51.5t-59.5 39.5
q-28 12 -46 22.5t-38.5 27t-30.5 38.5t-10 49q0 54 42.5 92t109.5 38q48 0 88 -18q6 -15 13 -50.5t9 -55.5z" id="x73"></path></g>
</svg>) for all the nuclei discussed in this paper.</table>

Advances in High Energy Physics

Neutrinoless Double β⁺/EC Decays

Figure 8

Advances in High Energy Physics

Neutrinoless Double β+/EC Decays

Figure 8

Neutrinoless Double β⁺/EC Decays