How are the particles in the LKP scenario initially distributed?

• A. 50% within the radius error, 45% within twice the radius error, 5% up to three times radius error
• B. 50% within the radius error only
• C. 60% within the radius error and 40% within twice radius error
• D. 100% within three times the radius error

Answer: (A)

This question is about how the initial particle distribution is spread across three concentric radial ranges defined by the radius error. In the LKP scenario, the particles are most concentrated near the center, with a decreasing number as you move outward, up to a cutoff.

The best choice describes that half of the particles lie inside one radius error, an additional 45% lie in the annulus between one and two radius errors, and the remaining 5% lie in the space between two and three radius errors. In other words, about 50% are within R, 95% are within 2R, and 100% are within 3R. This captures a strong central clustering with a small tail extending outward, which is a common way to model an initial localized distribution that still allows some particles to be found farther away.

The other options don’t reflect this stepped, central-heavy distribution. For example, all particles within the radius error would ignore the outward tail; a split like 60% inside R and 40% inside 2R implies no remaining particles beyond 2R; and saying all particles are within three times the radius error without detailing how they’re distributed inside those zones loses the clear central concentration and tail pattern described above.