Один β-спектр — несколько массовых порогов

Массовые состояния нейтрино у конца β-спектра

← Все апплеты К курсу

Задайте три массы. Каждый массовый компонент обрывается в своей точке, а детектор видит их взвешенную сумму.

resolvedEndpoint = 18.575
resolvedXMin = -12.5
resolvedXMax = -0.05

viewof resolvedMasses = {
  const control = html`<div class="resolved-mass-controls">
    <label>
      <span>${tex`m_1,\ \text{кэВ}`}</span>
      <output></output>
      <input name="mass1" type="range"
        min="0" max="12" step="0.5" value="0">
    </label>
    <label>
      <span>${tex`m_2,\ \text{кэВ}`}</span>
      <output></output>
      <input name="mass2" type="range"
        min="0" max="12" step="0.5" value="0">
    </label>
    <label>
      <span>${tex`m_3,\ \text{кэВ}`}</span>
      <output></output>
      <input name="mass3" type="range"
        min="0" max="12" step="0.5" value="10">
    </label>
  </div>`;

  const inputs = [...control.querySelectorAll("input")];
  const outputs = [...control.querySelectorAll("output")];

  function update(dispatch = true) {
    control.value = inputs.map(input => Number(input.value));
    outputs.forEach((output, i) => {
      output.textContent = String(control.value[i]).replace(".", ",");
    });
    if (dispatch) {
      control.dispatchEvent(new Event("input", {bubbles: true}));
    }
  }

  inputs.forEach(input => {
    input.addEventListener("input", () => update());
  });
  update(false);
  return control;
}

resolvedWeights = [1 / 3, 1 / 3, 1 / 3]

resolvedPhaseSpace = (x, mass) => {
  const neutrinoEnergy = -x;
  if (neutrinoEnergy < mass) return 0;
  return neutrinoEnergy * Math.sqrt(
    neutrinoEnergy * neutrinoEnergy - mass * mass
  );
}

resolvedRate = x => resolvedMasses.reduce(
  (sum, mass, i) =>
    sum + resolvedWeights[i] * resolvedPhaseSpace(x, mass),
  0
)

resolvedNorm = resolvedRate(resolvedXMin)
resolvedX = Array.from({length: 801}, (_, i) =>
  resolvedXMin + (resolvedXMax - resolvedXMin) * i / 800
)

resolvedData = resolvedX.map(x => ({
  x,
  y: resolvedRate(x) / resolvedNorm
}))

resolvedComponents = resolvedMasses.map((mass, i) =>
  resolvedX
    .map(x => ({
      x,
      y: resolvedWeights[i] * resolvedPhaseSpace(x, mass) / resolvedNorm
    }))
    .filter(d => d.y > 0)
)

resolvedThresholds = [...new Set(
  resolvedMasses
    .filter(mass => mass > 0)
    .map(mass => Number(mass.toFixed(1)))
)]

resolvedSuperscript = value => {
  const symbols = {
    "-": "⁻",
    "0": "⁰",
    "1": "¹",
    "2": "²",
    "3": "³",
    "4": "⁴",
    "5": "⁵",
    "6": "⁶",
    "7": "⁷",
    "8": "⁸",
    "9": "⁹"
  };
  return String(value)
    .split("")
    .map(character => symbols[character])
    .join("");
}

resolvedPowerLabel = value => {
  const exponent = Math.log10(value);
  if (Math.abs(exponent - Math.round(exponent)) > 1e-8) return "";
  return exponent === 0
    ? "1"
    : `10${resolvedSuperscript(Math.round(exponent))}`;
}

resolvedPlot = Plot.plot({
  width: 1040,
  height: 270,
  marginTop: 18,
  marginRight: 25,
  marginBottom: 45,
  marginLeft: 82,
  style: {
    background: "#ffffff",
    color: "#111111",
    fontSize: "20px"
  },
  x: {
    axis: "bottom",
    label: null,
    domain: [resolvedXMin, 0],
    ticks: 7,
    grid: true
  },
  y: {
    axis: "left",
    label: null,
    type: "log",
    domain: [1e-3, 1.1],
    ticks: 7,
    grid: true,
    tickFormat: resolvedPowerLabel
  },
  marks: [
    ...resolvedComponents.map(component => Plot.line(component, {
      x: "x",
      y: "y",
      stroke: "#777777",
      strokeWidth: 2,
      strokeDasharray: "6,5",
      clip: true
    })),
    Plot.line(resolvedData, {
      x: "x",
      y: "y",
      stroke: "#4ea1ff",
      strokeWidth: 4,
      clip: true
    }),
    Plot.ruleX(resolvedThresholds.map(mass => -mass), {
      stroke: "#ffb347",
      strokeDasharray: "7,5",
      strokeWidth: 2.5
    }),
    Plot.frame({stroke: "#111111"})
  ]
})

html`
<div class="spectrum-panel">
  <div class="spectrum-legend">
    <span>
      <i class="spectrum-swatch spectrum-swatch-massless"></i>
      сумма
    </span>
    <span>
      <i class="spectrum-swatch" style="background:#777777"></i>
      вклады ${tex`m_i`}
    </span>
    <span>
      ${tex`|V_{ei}|^2=\frac13`}
    </span>
  </div>
  <div class="spectrum-plot-row">
    <div class="spectrum-y-label">
      ${tex`\dfrac{1}{C(E)}\dfrac{d\Gamma}{dE}\;(\text{отн. ед.})`}
    </div>
    <div class="spectrum-plot-host">${resolvedPlot}</div>
  </div>
  <div class="spectrum-x-label">${tex`E-E_0\;(\text{кэВ})`}</div>
</div>`