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Theory of DM-atom Interactions Oren Slone, Princeton University - PowerPoint PPT Presentation

Theory of DM-atom Interactions Oren Slone, Princeton University Non CDM simulations 1 Theory of DM - bound nucleus Interactions 2 <latexit


  1. Theory of DM-atom Interactions Oren Slone, Princeton University Non ΛCDM simulations 1

  2. Theory of DM - “bound nucleus” Interactions 2

  3. <latexit sha1_base64="geFjEgqEJMQ/Gb4LrJawZ+6eY6Y=">ACEHicbVDJSgNBEO1xjXGLevTSGMR4CTMq6DG4gDcjmBjIhFDTqWhjz0J3jSQM+Qv/oXD4p49ejNv7ETc3B7UPB4r4qekGipCHX/XAmJqemZ2Zzc/n5hcWl5cLKat3EqRZYE7GKdSMAg0pGWCNJChuJRgDhZfBzdHQv7xFbWQcXVA/wVYIV5HsSgFkpXZhyz9GRcBPuA9JouMe90OgawEqOxuUfMIeZVgfbLcLRbfsjsD/Em9MimyMarvw7ndikYkVBgTNzE2ploEkKhYO8nxpMQNzAFTYtjSBE08pGDw34plU6vBtrWxHxkfp9IoPQmH4Y2M7htea3NxT/85opdQ9amYySlDASX4u6qeIU82E6vCM1ClJ9S0BoaW/l4ho0CLIZ5m0I3u+X/5L6TtnbLe+c7xUrh+M4cmydbAS89g+q7BTVmU1Jtgde2BP7Nm5dx6dF+f1q3XCGc+sR9w3j4BN46cuA=</latexit> Why Bound States? In - elastic to extract more energy. Chemical bonds typically have ∆ E ≈ O (eV) 3

  4. <latexit sha1_base64="8PBQbwtvxP0fmNwHgYWrYPjAKb4=">ACAXicbVDLSsNAFJ34rPUVdSO4GSyCq5JUQTdCUQSXFewDmhAm0k7dGYSZiZiCXjr7hxoYhb/8Kdf+OkzUJbD1w4nHMv94TJowq7Tjf1sLi0vLKamtvL6xubVt7+y2VJxKTJo4ZrHshEgRgVpaqoZ6SIB4y0g6HV7nfvidS0Vjc6VFCfI76gkYUI2kwN6/DjJPckgetERYj+EF5IGHBzSwK07VmQDOE7cgFVCgEdhfXi/GKSdCY4aU6rpOov0MSU0xI+OylyqSIDxEfdI1VCBOlJ9NPhjDI6P0YBRLU0LDifp7IkNcqREPTSdHeqBmvVz8z+umOjr3MyqSVBOBp4uilEdwzwO2KOSYM1GhiAsqbkV4gHKozChlU0I7uzL86RVq7on1drtaV+WcRAgfgEBwDF5yBOrgBDdAEGDyCZ/AK3qwn68V6tz6mrQtWMbMH/sD6/AG39pZq</latexit> <latexit sha1_base64="zgfkIsgAhVtTZV2Jltb3alYGwe8=">ACHXicbZDLSsNAFIYn9V5vVZduBovgqiS1oCsRpeCygr1AU8JkOrGDM0mYORFLyIu48VXcuFDEhRvxbZykXWjrgWE+/v8cZs7vx4JrsO1vq7SwuLS8srpWXt/Y3Nqu7Ox2dJQoyto0EpHq+UQzwUPWBg6C9WLFiPQF6/p3l7nfvWdK8yi8gXHMBpLchjzglICRvEqj6aWukpg9gCIUMnyG3cBQKj2Xjnhm7sInEMksw81C9SpVu2YXhefBmUIVTavlVT7dYUQTyUKgmjd+wYBilRwKlgWdlNIsJvSO3rG8wJLpQVpsl+FDowxEClzQsCF+nsiJVLrsfRNpyQw0rNeLv7n9RMITgcpD+MEWEgnDwWJwBDhPCo85IpREGMDhCpu/orpiOQxmUDLJgRnduV56NRrznGtft2onl9M41hF+gAHSEHnaBzdIVaqI0oekTP6BW9WU/Wi/VufUxaS9Z0Zg/9KevrBx2jo8=</latexit> Extracting the Energy Scattering Absorption O(eV) O(eV) m χ E extract > E χ E extract = m χ m atom 4

  5. <latexit sha1_base64="ExjK3xeLws1/E+0ADsKMk9DB8=">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</latexit> <latexit sha1_base64="fsupoAcLKcstcPsgYmXqC2ty8Ec=">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</latexit> How this works for Scattering |1> |0> ✓ m χ E extract ≈ q 2 + ~ q 2 ◆ q · ∆ ~ ∆ p p m χ E χ E extract ≈ E χ + ≈ ≈ m atom m atom m atom v χ m atom m atom 5

  6. <latexit sha1_base64="M50X/b0t9bSXmlICcOAr7eX/mU=">ACDHicbVDLSgNBEJz1GeMr6tHLYBC8GHajoBchKILHCOYB2RBmJ51kyOyDmV4xLPkAL/6KFw+KePUDvPk3ziZ70MSCgaKqmp4uL5JCo21/WwuLS8srq7m1/PrG5tZ2YWe3rsNYcajxUIaq6TENUgRQ4ESmpEC5nsSGt7wKvUb96C0CIM7HEXQ9lk/ED3BGRqpUyhedxJX+RQeUDGOY3pB7ZJz7NjURaMlFOpjk7JL9gR0njgZKZIM1U7hy+2GPYhQC6Z1i3HjrCdMIWCSxjn3VhDxPiQ9aFlaMB80O1kcsyYHhqlS3uhMi9AOlF/TyTM13rkeybpMxzoWS8V/NaMfbO24kIohgh4NFvVhSDGnaDO0KBRzlyBDGlTB/pXzA0lZMf3lTgjN78jypl0vOSal8e1qsXGZ15Mg+OSBHxCFnpEJuSJXUCeP5Jm8kjfryXqx3q2PaXTBymb2yB9Ynz8ABpmt</latexit> An example: Di-Atomic Molecules m 1 m 1 m 2 q m 2 E extract = 0 . 1 − 10 eV 6

  7. <latexit sha1_base64="ZvpSpr8cE4hT3K/H7nqv3wV9750=">ACQnicbZBLSwMxFIUz9VXra9Slm2ARXJWZKuhGKLpxWcE+pFNLJr1tQ5PMkGSEMva3ufEXuPMHuHGhiFsXpo9FbT0QOJzvXpKcMOZMG897dTJLyura9n13Mbm1vaOu7tX1VGiKFRoxCNVD4kGziRUDMc6rECIkIOtbB/NeK1B1CaRfLWDGJoCtKVrMoMTZquXePQbnHWmgBYRH94HsWICAkVklwO+wDNcJnSez1CYy037xW8sfCi8acmj6Yqt9yXoB3RIA0lBOtG74Xm2ZKlGUwzAXJBpiQvukCw1rJRGgm+m4giE+skbdyJljzR4nM5upERoPRChnRTE9PQ8G4X/sUZiOufNlMk4MSDp5KJOwrGJ8KhP3GYKqOEDawhVzL4V0x5RhBrbes6W4M9/edFUiwX/pFC8Oc2XLqd1ZNEBOkTHyEdnqISuURlVEVP6A19oE/n2Xl3vpzvyWjGme7soz9yfn4B13Syvg=</latexit> Diatomic Molecules Potential Energy Born Oppenheimer | Φ 0 mol i = | Φ 0 nuc i | Φ 0 e i 7

  8. <latexit sha1_base64="sCfPdYkP0/AsgCycFS/4EbSY0a0=">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</latexit> <latexit sha1_base64="9NlrUgnWkFloTRryG+464+x8Is=">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</latexit> <latexit sha1_base64="+cq0BivwovniLdCH3W+VcEe7sr4=">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</latexit> <latexit sha1_base64="UpOcxKMRyuPe/6WR8oE1TzrvA=">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</latexit> The Scattering Cross Section qdq Z f 2 P N | F DM ( q ) | 2 | F target ( q ) | 2 η [ v min ( q )] h σ v χ i / ¯ σ n 2 µ 2 χ n |M 2 → 2 ( q ) | 2 | F DM ( q ) | 2 ≡ |M 2 → 2 ( q 2 = q 2 DM Target 0 ) | 2 σ n ≡ |M 2 → 2 ( q 2 = q 2 0 ) | 2 Form Factor Form Factor ¯ 16 π ( m χ + m n ) 2 Z ∞ f ( ~ v χ ) V elocity d 3 v χ ⌘ [ v min ( q )] ≡ v χ Distribution v min 8

  9. <latexit sha1_base64="7+0yEs5m3OedItkjfp8kXaDL7M8=">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</latexit> <latexit sha1_base64="pvOgwjv3wicS2nlg60747+GmJPk=">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</latexit> The Form Factor WaveFunction Overlap for l = 90 Prob. to Transition 0.6 0.4 0.2 with E extract : 6 r @ a 0 D 2 3 4 5 - 0.2 - 0.4 2 � � Z | h Ψ f | H int | Ψ i i | 2 / | F target ( q ) | 2 ⌘ d 3 re i q · r Ψ ∗ � � f ( r ) Ψ i ( r ) � � � � Dictates the q-E Relation q 2 Energy Conservation: E extract = ~ v χ · ~ q − 2 µ χ target 9

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